Question

A rectangular shape has a length 4 cm less than five times its width. The perimeter is 160 cm. Find its length and width.

A) Length = 30 cm, Width = 6 cm
B) Length = 20 cm, Width = 8 cm
C) Length = 35 cm, Width = 5 cm
D) Length = 25 cm, Width = 10 cm

Answer 1

The length is 66 cm and the width is 14 cm.

Step-by-step explanation:

To find the length and width of the rectangular shape, we can use the given information. Let's assume the width as 'w', then the length would be 5w - 4 cm, based on the given condition.

The perimeter of a rectangle can be calculated by adding the lengths of all four sides. If we replace the length and width in the perimeter formula, we get: 2(5w - 4) + 2w = 160 cm.

Simplifying this equation, we get: 10w - 8 + 2w = 160. Combining like terms, we get: 12w - 8 = 160. Adding 8 to both sides, we get: 12w = 168. Lastly, dividing both sides by 12, we find that w = 14.

Substituting this value of 'w' back into the length equation, we find the length = 5(14) - 4 = 66 cm.