Question

The perimeter of a rectangle is 76 cm. If the length is eight more than four times its width, what are the dimensions of the rectangle?

a. Length = 14 cm, Width = 18 cm
b. Length = 24 cm, Width = 5 cm
c. Length = 20 cm, Width = 9 cm
d. Length = 16 cm, Width = 10 cm

Answer 1

The dimensions of the rectangle are Length = 16 cm, Width = 2 cm.

Step-by-step explanation:

To find the dimensions of the rectangle, we need to set up an equation using the given information. Let's call the width of the rectangle 'w', so the length would be '4w + 8' since it is eight more than four times the width. The perimeter is given as 76 cm, so we can set up the equation: 2(w + 4w + 8) = 76. Simplifying this equation, we get 10w + 16 = 38, and solving for 'w', we find that w = 2. Plugging this value back into the length equation, we find the length as 4(2) + 8 = 16 cm. Therefore, the dimensions of the rectangle are Length = 16 cm, Width = 2 cm.