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###### Maths question - Solving quadratics

2 years ago

The question is: The diagram shows two joined rectangles. The total area of the compound shape ABCDEF = 36cm^2 (squared) . By considering the areas of the two rectangles, show that 2x^2 -5x -18 = 0 and hence find the value of the length AB.

Note: Please make sure your final line only shows your final answer written as "AB = .."

A screenshot of the question is : https://prnt.sc/26jrzhq

There is a question on mathswatch which I definitely have the correct answer- but it only gives me 3/6 marks, so is it something to do with how I formatted the answer, or did I do something wrong in the working out? Can any of you help me spot the problem? The answer which I entered is:

AB = 9/2

given that In rectangle DEF

DE = (x-2) cm

EF = CD+AB

EF =2x+x

EF = 3x

Area of DEF rectangle = (x-2) (3x)

DEF = (x-2) (3x)

= 3x²-6x equation 1

In rectangle ABC

AB=x cm

CB =(x-4) cm

Area of ABC = (x)(x-4)

ABC²= x²-4x

ABCDEF² = 36cm²

36= 3x²-6x+ x²-4x

36= 4x²-10x

4x²-10x-36=0

4x² -18x + 8x - 36 = 0

4x(x + 2)-18(x + 2) = 0

(4x - 18)(x + 2) = 0

x = 18/4 or -2

x = -2

x = 18/4 or x = -2

dividing by 2

(4x²-10x-36=0)/2 = 2x²-5x-18=0

=2x²-5x-18=0 proved

2x²+4x-9x-18=0

2x(x+2)-9(x+2) =0

2x-9 =0

x+2=0

x=9/2

x=-2

side never be negative so we take positive value of

AB = 9/2

AB = 4.5

x = 9/2

Note: Please make sure your final line only shows your final answer written as "AB = .."

A screenshot of the question is : https://prnt.sc/26jrzhq

There is a question on mathswatch which I definitely have the correct answer- but it only gives me 3/6 marks, so is it something to do with how I formatted the answer, or did I do something wrong in the working out? Can any of you help me spot the problem? The answer which I entered is:

AB = 9/2

given that In rectangle DEF

DE = (x-2) cm

EF = CD+AB

EF =2x+x

EF = 3x

Area of DEF rectangle = (x-2) (3x)

DEF = (x-2) (3x)

= 3x²-6x equation 1

In rectangle ABC

AB=x cm

CB =(x-4) cm

Area of ABC = (x)(x-4)

ABC²= x²-4x

ABCDEF² = 36cm²

36= 3x²-6x+ x²-4x

36= 4x²-10x

4x²-10x-36=0

4x² -18x + 8x - 36 = 0

4x(x + 2)-18(x + 2) = 0

(4x - 18)(x + 2) = 0

x = 18/4 or -2

x = -2

x = 18/4 or x = -2

dividing by 2

(4x²-10x-36=0)/2 = 2x²-5x-18=0

=2x²-5x-18=0 proved

2x²+4x-9x-18=0

2x(x+2)-9(x+2) =0

2x-9 =0

x+2=0

x=9/2

x=-2

side never be negative so we take positive value of

AB = 9/2

AB = 4.5

x = 9/2

Original post by krugers123

The question is: The diagram shows two joined rectangles. The total area of the compound shape ABCDEF = 36cm^2 (squared) . By considering the areas of the two rectangles, show that 2x^2 -5x -18 = 0 and hence find the value of the length AB.

Note: Please make sure your final line only shows your final answer written as "AB = .."

A screenshot of the question is : https://prnt.sc/26jrzhq

There is a question on mathswatch which I definitely have the correct answer- but it only gives me 3/6 marks, so is it something to do with how I formatted the answer, or did I do something wrong in the working out? Can any of you help me spot the problem? The answer which I entered is:

AB = 9/2

given that In rectangle DEF

DE = (x-2) cm

EF = CD+AB

EF =2x+x

EF = 3x

Area of DEF rectangle = (x-2) (3x)

DEF = (x-2) (3x)

= 3x²-6x equation 1

In rectangle ABC

AB=x cm

CB =(x-4) cm

Area of ABC = (x)(x-4)

ABC²= x²-4x

ABCDEF² = 36cm²

36= 3x²-6x+ x²-4x

36= 4x²-10x

4x²-10x-36=0

4x² -18x + 8x - 36 = 0

4x(x + 2)-18(x + 2) = 0

(4x - 18)(x + 2) = 0

x = 18/4 or -2

x = -2

x = 18/4 or x = -2

dividing by 2

(4x²-10x-36=0)/2 = 2x²-5x-18=0

=2x²-5x-18=0 proved

2x²+4x-9x-18=0

2x(x+2)-9(x+2) =0

2x-9 =0

x+2=0

x=9/2

x=-2

side never be negative so we take positive value of

AB = 9/2

AB = 4.5

x = 9/2

Note: Please make sure your final line only shows your final answer written as "AB = .."

A screenshot of the question is : https://prnt.sc/26jrzhq

There is a question on mathswatch which I definitely have the correct answer- but it only gives me 3/6 marks, so is it something to do with how I formatted the answer, or did I do something wrong in the working out? Can any of you help me spot the problem? The answer which I entered is:

AB = 9/2

given that In rectangle DEF

DE = (x-2) cm

EF = CD+AB

EF =2x+x

EF = 3x

Area of DEF rectangle = (x-2) (3x)

DEF = (x-2) (3x)

= 3x²-6x equation 1

In rectangle ABC

AB=x cm

CB =(x-4) cm

Area of ABC = (x)(x-4)

ABC²= x²-4x

ABCDEF² = 36cm²

36= 3x²-6x+ x²-4x

36= 4x²-10x

4x²-10x-36=0

4x² -18x + 8x - 36 = 0

4x(x + 2)-18(x + 2) = 0

(4x - 18)(x + 2) = 0

x = 18/4 or -2

x = -2

x = 18/4 or x = -2

dividing by 2

(4x²-10x-36=0)/2 = 2x²-5x-18=0

=2x²-5x-18=0 proved

2x²+4x-9x-18=0

2x(x+2)-9(x+2) =0

2x-9 =0

x+2=0

x=9/2

x=-2

side never be negative so we take positive value of

AB = 9/2

AB = 4.5

x = 9/2

I will highlight bits I don't like:

given that In rectangle DEF [this is not four letters and it needs to be]

DE = (x-2) cm

[EF = CD+AB

EF =2x+x] not really needed

EF = 3x

Area of rectangle = (x-2) (3x) [three letters aren't a rectangle

DEF = (x-2) (3x) ..... write 3x(x - 2)

= 3x²-6x equation 1 ... delete equation 1 words

In rectangle ABC [again this is three letters - call it something else]

AB=x cm

CB =(x-4) cm

Area of ABC = (x)(x-4) .... write as x(x - 4)

ABC²= x²-4x ...... left square .. what is the power of 2 doing on the left?

ABCDEF² = 36cm² ... write Whole area

36= 3x²-6x+ x²-4x

36= 4x²-10x

4x²-10x-36=0 ... this is';t what you had to prove ... halve everything

4x² -18x + 8x - 36 = 0 ... delete all the rest

4x(x + 2)-18(x + 2) = 0

(4x - 18)(x + 2) = 0

x = 18/4 or -2

x = -2

x = 18/4 or x = -2

dividing by 2

(4x²-10x-36=0)/2 = 2x²-5x-18=0

=2x²-5x-18=0 proved .... all these equal signs are not needed

2x²+4x-9x-18=0

2x(x+2)-9(x+2) =0 no show factorised form then either x + 2 = 0 or .... rewrite

2x-9 =0

x+2=0

x=9/2

x=-2

side never be negative so we take positive value of

AB = 9/2

AB = 4.5

x = 9/2 not in correct form

EDIT it down as i suggest but Mathswatch is notoriously fussy

Reply 2

2 years ago

Original post by Muttley79

I will highlight bits I don't like:

given that In rectangle DEF [this is not four letters and it needs to be]

DE = (x-2) cm

[EF = CD+AB

EF =2x+x] not really needed

EF = 3x

Area of rectangle = (x-2) (3x) [three letters aren't a rectangle

DEF = (x-2) (3x) ..... write 3x(x - 2)

= 3x²-6x equation 1 ... delete equation 1 words

In rectangle ABC [again this is three letters - call it something else]

AB=x cm

CB =(x-4) cm

Area of ABC = (x)(x-4) .... write as x(x - 4)

ABC²= x²-4x ...... left square .. what is the power of 2 doing on the left?

ABCDEF² = 36cm² ... write Whole area

36= 3x²-6x+ x²-4x

36= 4x²-10x

4x²-10x-36=0 ... this is';t what you had to prove ... halve everything

4x² -18x + 8x - 36 = 0 ... delete all the rest

4x(x + 2)-18(x + 2) = 0

(4x - 18)(x + 2) = 0

x = 18/4 or -2

x = -2

x = 18/4 or x = -2

dividing by 2

(4x²-10x-36=0)/2 = 2x²-5x-18=0

=2x²-5x-18=0 proved .... all these equal signs are not needed

2x²+4x-9x-18=0

2x(x+2)-9(x+2) =0 no show factorised form then either x + 2 = 0 or .... rewrite

2x-9 =0

x+2=0

x=9/2

x=-2

side never be negative so we take positive value of

AB = 9/2

AB = 4.5

x = 9/2 not in correct form

EDIT it down as i suggest but Mathswatch is notoriously fussy

given that In rectangle DEF [this is not four letters and it needs to be]

DE = (x-2) cm

[EF = CD+AB

EF =2x+x] not really needed

EF = 3x

Area of rectangle = (x-2) (3x) [three letters aren't a rectangle

DEF = (x-2) (3x) ..... write 3x(x - 2)

= 3x²-6x equation 1 ... delete equation 1 words

In rectangle ABC [again this is three letters - call it something else]

AB=x cm

CB =(x-4) cm

Area of ABC = (x)(x-4) .... write as x(x - 4)

ABC²= x²-4x ...... left square .. what is the power of 2 doing on the left?

ABCDEF² = 36cm² ... write Whole area

36= 3x²-6x+ x²-4x

36= 4x²-10x

4x²-10x-36=0 ... this is';t what you had to prove ... halve everything

4x² -18x + 8x - 36 = 0 ... delete all the rest

4x(x + 2)-18(x + 2) = 0

(4x - 18)(x + 2) = 0

x = 18/4 or -2

x = -2

x = 18/4 or x = -2

dividing by 2

(4x²-10x-36=0)/2 = 2x²-5x-18=0

=2x²-5x-18=0 proved .... all these equal signs are not needed

2x²+4x-9x-18=0

2x(x+2)-9(x+2) =0 no show factorised form then either x + 2 = 0 or .... rewrite

2x-9 =0

x+2=0

x=9/2

x=-2

side never be negative so we take positive value of

AB = 9/2

AB = 4.5

x = 9/2 not in correct form

EDIT it down as i suggest but Mathswatch is notoriously fussy

I only saw you highlight the "DEF" part, is that the only text I need to remove?

Original post by krugers123

I only saw you highlight the "DEF" part, is that the only text I need to remove?

No - highlighting got too awkward - read it through - far too much in the wrong order.

Reply 4

2 years ago

Original post by Muttley79

No - highlighting got too awkward - read it through - far too much in the wrong order.

Ok, but will that guarantee the other 3 marks? Doesn't mathswatch's API just scan the textarea and mark as to whether the correct things are included?

Original post by krugers123

Ok, but will that guarantee the other 3 marks? Doesn't mathswatch's API just scan the textarea and mark as to whether the correct things are included?

No - you've solved it before you got the equation it wanted

Original post by krugers123

Ok, but will that guarantee the other 3 marks? Doesn't mathswatch's API just scan the textarea and mark as to whether the correct things are included?

Have you sorted this?

Reply 7

1 year ago

Original post by Muttley79

Have you sorted this?

Yes, thank you

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