The length of a rectangle is 3 cm less than five times its width. Its perimeter is 102 cm. Find its length and width.
A) The length is 51 cm and the width is 11 cm.
B) The length is 42 cm and the width is 9 cm.
C) The length is 48 cm and the width is 9 cm.
D) The length is 46 cm and the width is 11 cm.
E) The length is 44 cm and the width is 12 cm.

Question

The length of a rectangle is 3 cm less than five times its width. Its perimeter is 102 cm. Find its length and width.
A) The length is 51 cm and the width is 11 cm.
B) The length is 42 cm and the width is 9 cm.
C) The length is 48 cm and the width is 9 cm.
D) The length is 46 cm and the width is 11 cm.
E) The length is 44 cm and the width is 12 cm.

Quizplus · Accepted Answer

The perimeter of a rectangle is given by the formula $P = 2l + 2w$, where $l$ is the length and $w$ is the width. Given that the length $l = 5w - 3$ and the perimeter $P = 102$, we can substitute the expression for $l$ into the perimeter formula to get $102 = 2(5w - 3) + 2w$. Simplifying, we get $102 = 10w - 6 + 2w$, which simplifies further to $108 = 12w$, leading to $w = 9$. Substituting $w = 9$ back into the expression for $l$, we get $l = 5(9) - 3 = 45 - 3 = 42$. Therefore, the width is 9 cm and the length is 42 cm.

The Length of a Rectangle Is 3 Cm Less Than