Question

A rectangle's perimeter is 80 ft. Its length is 4 ft shorter than three times its width. Use an equation to find the rectangle's length and width

Answer 1

Question:

A rectangle's perimeter is 80 ft. Its length is 4 ft shorter than three times its width. Use an equation to find the rectangle's length and width​.

Solution:

Let's denote by L the length of the rectangle, and by W its width. Now, if the length is 4 ft shorter than three times its width, we have the following diagram:

Then, we have the following equation:

$2(3W-4)\text{ + 2W = 80 = perimeter}$

this is equivalent to:

$6W\text{ -8 + 2W = 80}$

this is equivalent to:

$8W\text{ = 80 +8 = 88}$

solving for W, we obtain:

$W\text{ = }\frac{88}{8}=\text{ 11}$

then, the width is 11 and the length would be:

$L\text{ = 3W -4 = 3(11) -4 = 29}$

then, we can conclude that the correct answer is:

Length = 29

Width = 11