Question

The areas of the square and the rectangle are equal.
What is the value of x?

Answer 1

x=12

Explanation:

Area of the square

A = x^2

Area of the rectangle

A = (2x-8) (x-3)

Foil

A = 2x^2 -6x -8x +24

= 2x^2 -14x+24

The areas are equal

x^2 = 2x^2 -14x+24

Subtract x^2 from each side

x^2 - x^2 = 2x^2-x^2 -14x+24

0 = x^2 -14x -24

Factor

0 = (x-12) (x-2)

Using the xero product property

x-12= 0 x-2 =0

x=12 x=2

But looking at the rectangle

x-3 is a side length

2-3 is negative so x cannot equal 2

x=12