Question

a square has a side length of x. A rectangle has a length that is 4 inches longer than the square and a width that is 2 inches shorter than the square. If the areas of the square and rectangle are equal, what is the length of the rectangle?

Answer 1

Length of the rectangle is = 8 inches.

Explanation:

Given :

Area of square = Area of the rectangle

According to the question:

Length of the square be 'x'.

Its area = (Side)*(Side) =
`x^2` ...equation (i)

Length of the rectangle =
`(x+4)`

Width of the rectangle =
`(x-2)`

Area of the rectangle =Length * Width

⇒
`(x+4)(x-2)=x^2-2x+4x-8`

⇒
`x^2+2x-8` ...equation (ii)

Equating both the equation as area of both the figure are equal.

⇒
`x^2+2x-8=x^2`

⇒
`2x-8=0` ...subtracting
`x^2` both sides

⇒
`2x=8` ...dividing both sides with 2

⇒
`x=(8)/(2)=4` inches

Plugging the value of x=4 in the length of the rectangle.

We have,

⇒
`(x+4)=(4+4)=8`

So the length of the rectangle = 8 inches.