Question

Patty made a banner that has an area of 36 square inches,. The length and width of the banner are whole numbers. The length is 4 times greater than the width. What are the dimensions of the banner?

Answer 1

The length of the banner is 12 inches while the width of the banner is 3 inches

Explanation:

Here we have the area of the rectangular banner = 36 in²

Formula for the area of the banner is Length, L × Width, W

We are told the length is 4 times greater than the width.

That is, L = 4·W

Therefore, the area of the banner = L × W = 4·W × W = 4·W² = 36 in²

∴ W = √(36/4) = 3 inches

L = 4·W = 4 × 3 inches = 12 inches

Therefore, the dimensions of the banner are

Length of banner = 12 inches

Width of banner = 3 inches.

Answer 2

Answer: width= 3 inches; length= 12 inches.

Explanation:

From the question, the length is 4 times greater than the width.

Let the width of the banner be represented by y.

Since the length is 4 times greater than the width. It will be denoted as:

Length= 4 × y = 4y

Since area= length×width

4y × y = 36

4y^2 = 36

Divide both side by 4

y^2 = 36/4

y^2 = 9

We have to find the square root of 9

y= √9

y = 3

The width is 3 inches.

The length will be: (3×4) = 12 units.