Question

the length of a rectangle is 3 times the width, and the rectangle has a perimeter of 166 yards. what is its length? you do not need to include the unit measurement or unit type. only the numerical answer is necessary. round to the nearest tenth if necessary. review the linked section of the prealgebra textbook for problem help

Explanation:

Step1: Set up variables

Let the width of the rectangle be \( w \). Then the length \( l = 3w \). The formula for the perimeter of a rectangle is \( P=2(l + w) \). Substitute \( l = 3w \) into the perimeter formula: \( P=2(3w+w) \).

Step2: Solve for \( w \)

Given \( P = 166 \), we have \( 166=2(3w + w) \). Simplify the right - hand side: \( 166=2\times4w=8w \). Then \( w=\frac{166}{8}=20.75 \).

Step3: Find the length

Since \( l = 3w \), substitute \( w = 20.75 \) into the equation. So \( l=3\times20.75 = 62.25 \).

Answer:

\( 62.3 \) (rounded to the nearest tenth)