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 inches.

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.

Answer 1

D.

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

Explanation:

Answer 2

D.

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

Explanation:

Let x inches be the widht of the section. If the length is 3 times the width, then the length is 3x inches.

The perimeter of the rectangle is

`P=2(\text{width + length})`

Hence,

`P=2(x+3x)=2\cdot 4x=8x`

The perimeter of the section must be less than 320 inches, so

`8x<320\\ \\x<40\\ \\3x<120`