maths

The diagram shows two rectangles. The total area of the compound shape ABCDEF is 36cm^2.

By considering the areas of the two rectangles, show that 2x^2-5x-18=0 and hence find the value of the length AB.

OP

This is the diagram

Original post by hugjai

This is the diagram

Form your equation by reading the question, find the area of each shape individually, for example if i had a rectangle with sides x and x+2, the area A=x(x+2). Be careful with the length of EF, it is not 2x. This is a common mistake. If you are having any trouble just show me what you have done so far!

Reply 3

Beerstaff

1

Find the area of each rectangle individually. Add the two expressions and put them equal to 36. Halve the lot and you'll see what to do next

Reply 4

hugjai

OP

2

Original post by Beerstaff

Find the area of each rectangle individually. Add the two expressions and put them equal to 36. Halve the lot and you'll see what to do next

I've found the area of the rectangles and added them to equate it to 36. I got 4x^2 - 10x = 36. But what do you mean by halve the lot? Am I supposed to take the 36 over and equate it to 0 (4x^2 - 10x - 36 = 0) and then factorise it?

Reply 5

hugjai

OP

2

Original post by Azim Patel

Form your equation by reading the question, find the area of each shape individually, for example if i had a rectangle with sides x and x+2, the area A=x(x+2). Be careful with the length of EF, it is not 2x. This is a common mistake. If you are having any trouble just show me what you have done so far!

This is what I've done so far

area of the big rectangle: 2x + x = 3x
3x ( x - 2 ) = 3x^2 - 6x

area of the small rectangle: x ( x - 4) = x^2 - 4x

I added them together: 3x^2 - 6x + x^2 - 4x = 4x^2 -10x

then equate them to 36: 4x^2 -10x = 36

Then I took the 36 to the left side of the equation and equate it to 0: 4x^2 -10x - 36 = 0

Then I factorised it: -36 * 4 = -144 -10

8 * -18 = -144
8 - 18 = -10

4x^2 + 8x - 18x -36 = 0

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

4x - 18 = 0 x + 2 = 0
4x = 18 x = -2
x= 18/4

This is where that I'm stuck, the answer is not 18/4 or -2

I got 2 marks for doing just that, however, I don't know what else to do to get 6 marks

Am I suppose to work out the equation 2x^2-5x-18=0? If so, I got x = 9/2 and x = -2

(edited 5 years ago)

Reply 6

Muttley79

20

Original post by hugjai

This is what I've done so far

area of the big rectangle: 2x + x = 3x
3x ( x - 2 ) = 3x^2 - 6x

area of the small rectangle: x ( x - 4) = x^2 - 4x

I added them together: 3x^2 - 6x + x^2 - 4x = 4x^2 -10x

then equate them to 36: 4x^2 -10x = 36

Then I took the 36 to the left side of the equation and equate it to 0: 4x^2 -10x - 36 = 0

I got 2 marks for doing just that, however, I don't know what else to do to get 6 marks

Am I suppose to work out the equation 2x^2-5x-18=0? If so, I got x = 9/2 and x = -2

If you halve the equation you found you get the right one.

How could you simplify your answer 18/4?

Reply 7

AzimP

11

Original post by Muttley79

If you halve the equation you found you get the right one.

How could you simplify your answer 18/4?

Your equation is correct 4x^2 -10x -36=0, just divide throughout by 2, since you want to get 2x^2 -5, -18=0, x=18/4 is correct, maybe the mark scheme says 9/2 or 4.5 but these are all equivalent

Original post by hugjai

This is what I've done so far

area of the big rectangle: 2x + x = 3x
3x ( x - 2 ) = 3x^2 - 6x

area of the small rectangle: x ( x - 4) = x^2 - 4x

I added them together: 3x^2 - 6x + x^2 - 4x = 4x^2 -10x

then equate them to 36: 4x^2 -10x = 36

Then I took the 36 to the left side of the equation and equate it to 0: 4x^2 -10x - 36 = 0

Then I factorised it: -36 * 4 = -144 -10

8 * -18 = -144
8 - 18 = -10

4x^2 + 8x - 18x -36 = 0

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

4x - 18 = 0 x + 2 = 0
4x = 18 x = -2
x= 18/4

This is where that I'm stuck, the answer is not 18/4 or -2

I got 2 marks for doing just that, however, I don't know what else to do to get 6 marks

Am I suppose to work out the equation 2x^2-5x-18=0? If so, I got x = 9/2 and x = -2

Reply 8

Muttley79

20

Original post by Azim Patel

...

Why did you quote me?I know the equation is correct - I am waiting for the OP to return.

Reply 9

AzimP

11

Original post by Muttley79

Why did you quote me?I know the equation is correct - I am waiting for the OP to return.

Mistake, sorry bro

Reply 10

hugjai

OP

2

Original post by Muttley79

If you halve the equation you found you get the right one.

How could you simplify your answer 18/4?

You divide the numerator and denominator by 2 to get 9/2

Reply 11

Muttley79

20

Original post by hugjai

You divide the numerator and denominator by 2 to get 9/2

have you got all the marks now? Is this Mathswatch?

Reply 12

sqrt of 5

19

Original post by Muttley79

have you got all the marks now? Is this Mathswatch?

It is indeed, I did that question a few days ago

Reply 13

Muttley79

20

Original post by sqrt of 5

It is indeed, I did that question a few days ago

Terrible isn't it?!'ve helped so many people try to get all the marks when they are correct because it's looking for specific words or format ...

Reply 14

sqrt of 5

19

Original post by Muttley79

Terrible isn't it?!'ve helped so many people try to get all the marks when they are correct because it's looking for specific words or format ...

I know right! I remember last week I couldn't get full marks to a question because I wrote x ³instead of x³ lol

Reply 15

Beerstaff

1

Yep, you've done it correctly. Bring the 36 over to make =0 on the right Hand- side. Then halve everything to make the equation in the form that the question wanted. Explicitly 2x^2-5x-18=0Then factorise and solve as you did to make -2 and 4.5The answer must be 4.5 as you can't have a negative length.