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simple maths problem

okay a very simple problem but i cant quite get my head around the logic behind the correct solution

A square, s, has its length increased by 10 units and its width decreased by 10, to form rectangle R.

Is the perimeter of rectangle R less than, equal to, or greater than square s

Is the area of rectangle R less than, equal to, or greater than square S

- the area decreases and i calculate this obviously if dimensions were given, but i really dont understand *why*
Reply 1
Avatar for vvlp
vvlp
10
So the perimeter of the square is 4x, whereas the perimeter of the rectangle is 2(x-10) + 2(x+10)

This multiplies out to get you (2x-20) + (2x+20) = 4x, therefore the perimeter is the same.

By this logic you can work out the area of the shapes.

S = x^2
R = (x+10)(x-10) = x^2 - 100, therefore the area of the rectangle is smaller.

Does this answer your question?
(edited 8 years ago)
Original post by vvlp
So the perimeter of the square is 4x, whereas the perimeter of the rectangle is 2(x-10) + 2(x+10)?
If I'm correct, this multiplies out to get you (2x-20) + (2x+20) = 4x, therefore the perimeter is the same, correct?
If I've understood the question properly, by this logic you can work out the area of the shapes.
S = x^2
R = (x+10)(x-10) = x^2 - 100, therefore the area of the rectangle is smaller.
Does this answer your question (assuming I have read and understood the question properly)?


fantastic. its that quadratic expansion that i never recognized

thanks a million
Reply 3
Avatar for vvlp
vvlp
10
Original post by hi-zen-berg
fantastic. its that quadratic expansion that i never recognized
thanks a million

Glad I could help!
Reply 4
Avatar for saeed97
saeed97
5
Original post by hi-zen-berg
okay a very simple problem but i cant quite get my head around the logic behind the correct solution

A square, s, has its length increased by 10 units and its width decreased by 10, to form rectangle R.

Is the perimeter of rectangle R less than, equal to, or greater than square s

Is the area of rectangle R less than, equal to, or greater than square S

- the area decreases and i calculate this obviously if dimensions were given, but i really dont understand *why*


Perimeter remains the same.
Area of square is greater than the area of the rectangle.
Too late to explain why.
Original post by saeed97
Perimeter remains the same.
Area of square is greater than the area of the rectangle.
Too late to explain why.


Genius


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Reply 6
Avatar for saeed97
saeed97
5
Original post by Ad109


Aww thanx xoxoxo
Original post by saeed97
Aww thanx xoxoxo


Hm with that reply? Can I take it back, I lied you see asiff


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Reply 8
Avatar for saeed97
saeed97
5
Original post by Ad109
Hm with that reply? Can I take it back, I lied you see asiff


Posted from TSR Mobile


I am a genius and theres nothing you can do.

Spoiler

Reply 9
Avatar for TeeEm
TeeEm
19
Original post by Ad109
Hm with that reply? Can I take it back, I lied you see asiff
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Original post by saeed97
I am a genius and theres nothing you can do.

Spoiler




bedtime both ...
Reply 10
Avatar for saeed97
saeed97
5
Original post by TeeEm
bedtime both ...


But my mommy said i can stay up today.
Original post by saeed97
I am a genius and theres nothing you can do.

Spoiler



Come 1v1 outside the masjid after taraweeh


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