Thread: Rectangle with given sides (in terms of x) and diagonal.

I have a rectangle of sides x and y
x+y=5
The diagonal of the rectangle is 4
Show that 2x^2-10x+9=0

I did

so i tried doing a simultaneous equation by cancelling out the y^2 first
I did the x+y=10 times (x-y)

So I added them together


Now I'm stuck. What have I done wrong?

Originally Posted by Mukilab

I have a rectangle of sides x and y
x+y=5
The diagonal of the rectangle is 4
Show that 2x^2-10x+9=0

I did

so i tried doing a simultaneous equation by cancelling out the y^2 first
I did the x+y=10 times (x-y)

So I added them together


Now I'm stuck. What have I done wrong?

x+y=5 or x+y=10 ?

sorry, x+y=5, got confused because it previously asked me to show that x+y=5 (2x+2y=10=perimeter)

Originally Posted by Mukilab

I have a rectangle of sides x and y
x+y=5
The diagonal of the rectangle is 4
Show that 2x^2-10x+9=0

I did

so i tried doing a simultaneous equation by cancelling out the y^2 first
I did the x+y=10 times (x-y)

So I added them together


Now I'm stuck. What have I done wrong?

x^2 + y^2 = 4^2 .... (1)

x + y = 5 => y = 5 - x .... (2)

Substitute (2) into (1), expand, simplify and re-arrange.