Question

select the correct answer.
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 inches.
length
width
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 of the rectangle be \( w \) inches. Then the length \( l = 3w \) inches.

Step2: Recall perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \).

Step3: Substitute length and apply inequality

Substitute \( l = 3w \) into the perimeter formula: \( P = 2(3w + w)=2(4w) = 8w \).
We know that \( P < 320 \), so \( 8w < 320 \).

Step4: Solve for width

Divide both sides of the inequality \( 8w < 320 \) by 8: \( w < \frac{320}{8}=40 \).

Step5: Solve for length

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.