Don L. answered • 11/27/18

Fifteen years teaching and tutoring basic math skills and algebra

Hi Dylan, let L represent the length of the rectangle. Then 1/2 * L + 10 represents the width of the rectangle.

Equation to solve:

L * (1/2 L + 10) = 64

Solving:

L^{2} / 2 + 10L = 64

Multiply entire equation by 2 to clear the fraction:

L^{2} + 20L = 164

Rewrite in quadratic form:

L^{2} + 20L - 164 = 0

Use the quadratic formula to solve:

x = 5.099, or 5.1 rounded and x = -25.099

Discard the second solution since x cannot be negative.

The width of the rectangle equal 1/ 2 the length + 10:

1 / 2 (5.1) + 10 = 12.55

The width of the rectangle is 12.55 feet squared.

Check:

5.1 * 12.55 = 64

64 ~ 64 , caused by rounding error.

Questions?