Question

If one side of a rectangle is five less than the other side and the perimeter is 90 inches, find the area of the rectangle.

Answer 1

so given a rectangle
sides are
_x_
x-5|__|x-5
x

the perimeter is 90 inches
perimeter is
x + x + (x-5) + (x-5) = 90
combine like terms
2x + 2(x-5) = 90
distribute
2x + 2x-10 = 90
combine like terms
4x - 10 = 90
add 10 to both sides
4x= 100
divide both sides by 4
x = 25

now to find the length of a side
x is 25
and x-5 is 20

to check and see if that's right:
25 + 25 + 20 + 20 =?= 90
50 + 40 =?=
90 = 90

Now to find the area
A = b * h
so
x * (x-5)
substitute
25* 20
500
The area of the rectangle is 500

Hope this helps :)