A rectangle's length is twice its width. If the area is 72 square feet, what is the width?

A rectangle's length is twice its width. If the area is 72 square feet, what is the width?

• A. 6 ft
• B. 8 ft
• C. 9 ft
• D. 12 ft

Answer: (A)

To determine the width of the rectangle, let's denote the width as \( w \). Since the length is twice the width, we can express the length as \( 2w \). The area \( A \) of a rectangle is calculated using the formula: \[ A = \text{length} \times \text{width} \] Substituting the expressions for length and width into the area formula gives: \[ A = (2w) \times w = 2w^2 \] We know from the problem that the area is 72 square feet, so we set up the equation: \[ 2w^2 = 72 \] To solve for \( w^2 \), divide both sides by 2: \[ w^2 = \frac{72}{2} = 36 \] Next, take the square root of both sides to find \( w \): \[ w = \sqrt{36} = 6 \] Thus, the width of the rectangle is 6 feet. This answer makes sense in the context of the problem because if the width is 6 feet, the length, being twice the width, would be 12 feet.

To determine the width of the rectangle, let's denote the width as ( w ). Since the length is twice the width, we can express the length as ( 2w ).

The area ( A ) of a rectangle is calculated using the formula:

[

A = \text{length} \times \text{width}

]

Substituting the expressions for length and width into the area formula gives:

[

A = (2w) \times w = 2w^2

]

We know from the problem that the area is 72 square feet, so we set up the equation:

[

2w^2 = 72

]

To solve for ( w^2 ), divide both sides by 2:

[

w^2 = \frac{72}{2} = 36

]

Next, take the square root of both sides to find ( w ):

[

w = \sqrt{36} = 6

]

Thus, the width of the rectangle is 6 feet.

This answer makes sense in the context of the problem because if the width is 6 feet, the length, being twice the width, would be 12 feet.