Question

a rectangular section of granite is being cut so that the length is 3 times the width. the perimeter of the section must be less than 320 in
which statement is true?
a. the length of the granite must be at least 80 inches.
b. the length of the granite must be less than 100 inches.
c. the length of the granite must be at least 100 inches.
d. the length of the granite must be less than 120 inches.

Explanation:

Step1: Define variables

Let the width be \( w \) inches. Then the length \( l = 3w \) inches.

Step2: Use perimeter formula

The perimeter \( P \) of a rectangle is \( P = 2(l + w) \). Substitute \( l = 3w \) into the formula: \( P = 2(3w + w)=2(4w)=8w \).

Step3: Apply perimeter constraint

We know that \( P < 320 \), so \( 8w < 320 \). Solve for \( w \): divide both sides by 8, \( w < \frac{320}{8}=40 \).

Step4: Find length constraint

Since \( l = 3w \) and \( w < 40 \), then \( l = 3w < 3\times40 = 120 \). So the length must be less than 120 inches.

Answer:

D. The length of the granite must be less than 120 inches.