Question

A square has an unknown side length of x feet. It is transformed into a rectangle by increasing its length by 12 feet and decreasing its width by 4 feet.
(a) Determine a trinomial expression for the area of the new rectangle in terms of x. Create an area model to illustrate how you found your answer.

(b) If the area of the new rectangle is equal to the area of the original square, then find the numerical side length of the original square, x. Show how you found your answer.

Answer 1

Answer:

(a) $Area = x^2 + 8x - 48$

(b) $x = 6$

Step-by-step explanation:

Given

Let the side length of the square be x

So, the rectangle has:

$Length = x + 12$ -- increase by 12

$Width = x - 4$ --- decrease by 4

Solving (a): The area of the rectangle.

This is:

$Area = Length * Width$

$Area = (x + 12) *(x - 4)$

Open brackets

$Area = x^2 + 12x - 4x - 48$

$Area = x^2 + 8x - 48$

Solving (b): Find x

The area of the square is:

$Area = x^2$

If the rectangle has the same area, then:

$x^2 + 8x - 48 = x^2$

Collect like terms

$8x - 48 = x^2 - x^2$

$8x - 48 = 0$

$8x = 48$

Solve for x

$x = 6$