Question

Write an equation for the problem and then solve.

The perimeters of two rectangles are equal. The dimensions of one rectangle are 2x and x while the dimensions of the other rectangle are x + 12 and x - 3. What are the numerical dimensions of the rectangles? (Solve for x)



Answer: x =

Answer 1

• first rectangle: 18 by 9
• second rectangle 21 by 6
• x = 9

Explanation:

The perimeter in each case is double the sum of the side dimensions. Since the perimeters are equal, the sum of side dimensions will be equal:

2x +x = (x +12) +(x -3)

3x = 2x +9 . . . . . . . . collect terms

x = 9 . . . . . . . . . . . . . subtract 2x

Given this value of x, the dimensions of the first rectangle are ...

{2x, x} = {2·9, 9} = {18, 9}

And the dimensions of the second rectangle are ...

{x+12, x-3} = {9+12, 9-3} = {21, 6}