Question

A rectangular bin has a perimeter of 42 inches. The length of the bin is twice the width. Write and solve an equation to determine the length, in inches, of the bin. Then find the area, in square inches, of the bin.

Answer 1

Answer: Length of bin = 14 inches

Area of the bin = 98 inches²

Step-by-step explanation:

Perimeter of rectangle = 2 (length + width)

Let perimeter of the rectangular bin = 42 inches

Length (l) = 2x

Width (w) = x

2 (length + width) = 42 inches

2 (2x + x) = 42 inches

2 (3x) = 42 inches

6x = 42 inches

x = 42 ÷ 6 = 7 inches

Length (l) = 2x = 14 inches

Width (w) = x = 7 inches

Area = Length × width

Area of the bin = Length × width

= 14 × 7

= 98 inches²

Answer 2

Explanation:

So imagine a rectangle. The perimeter of a rectangle is 2w + 2l = perimeter. Because perimeter is the sides added up. It says the length is 2 times the width so use 2w. the width would just be w. Now add up the sides. 2w+2w+w+w which equals 6w. It states that the perimeter is 42 so now set 6w equal to 42 and solve for w. W would be 7 and that is the width. The length is 2(7) so length is 14 inches. Area would be 7 x 14 because area is length times width and so the area is 98 square units.