A rectangle has an area of 288 square feet. The width is 5 more than 3 times the length. Find the length and width, in feet, of the rectangle.

Answer 1

Hi Kristin,

A rectangle has an area of 288 square feet.

The width is 5 more than 3 times the length.

Find the length and width, in feet, of the rectangle.

Given:

1. Rectangle
2. area = 288 ft²
3. Width is 5 more than 3 times Length

Find:

1. Length and width in feet

Formulas/information:

1. the area of a rectangle is L x W
2. Let W = width
3. let L = length

First, convert "Width is 5 more than 3 times Length" into algebraic expression

5 more converts to +5 3 times length converts to 3L

1. W = 3L +5

Area = L x W

288 = L x (3L+5)

288 = 3L²+ 5L

0 = 3L²+ 5L - 288

Solve for L using quadratic formula

L = [-5 +/- sqrt (5²-4(3)(-288)] / 2(3)

L = [-5 +/- sqrt (3481)] / 6

L = [-5 +/- 59] / 6

L = 9 or L = -10.67

SInce the side length cannot be negative, the -10.67 value is not valid

So

L = 9 feet

W = 3L +5 = 3(9) + 5 = 32 feet

Verify L x W = 288

9 x 32 = 288

So it checks out!