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

The areas of the square and the rectangle are equal. What is the value of x?-example-1

1 Answer

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Answer:

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

User Bhupesh Parakh
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