finding the perimeter

Question

A rectangle has a perimeter of 44 inches. The length of the rectangle is 3 less than 4 times the width

Answer 1

I believe you are looking for the length and width measures.

Perimeter = 2L + 2W <----- L = length; W = width

Perimeter = 44 inches as given

Length = 4W - 3 due to the wording "3 less than 4 times width." 4 times width is 4w, and 3 less means subtract 3 from that.

So we have P = 44 ; L = 4W - 3

Let's solve the perimeter equation for W.

P = 2L + 2W

44 = 2 (4W - 3) + 2W

44 = 8W - 6 + 2W <-------------- Distributive Property: 2 x 4W = 8W; 2 x -3 = -6

44 = 10W - 6 <-------------- Combine like terms

50 = 10W <-------------- Add 6 to both sides

5 = W <-------------- Divide by 10 on both sides

Width = 5 inches.

Length = 4W - 3 = 4(5) - 3 = 20 - 3 = 17 inches

Dimensions: L = 17 in, W = 5 in