Question

Rectangle C is a special shape because its area is EQUAL to its perimeter. The side lengths of the rectangle are 2x and 7. Solve for x. If your answer is not an integer, write it as a DECIMAL when you type it in.

Answer 1

Because a square has four sides of equal length, the area is given by A = L2. If you know the area, you can immediately determine the length of each side, because it's the square root of the area.

Explanation:

Answer 2

x = 1.4

Explanation:

The area of a rectangle is A = (length)(width), and the perimeter is P = 2(length)+2(width). Replacing (length) with 2x and width with 7, and equating these two formulas, we get:

A = (2x)(7) = P = 2(2x) + 2(7)

Simplifying through multiplication:

14x = 4x + 14, which simplifies further to:

10x = 14, or x = 7/5, or 1.4

x = 1.4