Question

The length of a rectangle is one inch less than five times its width. If the perimeter of the rectangle is 46 inches, find its dimensions. Write your answer as two numbers separated by a comma

Answer 1

19,4 or 4,19

Explanation:

Let the width of the rectangle be 'w' in

According to the question length of the rectangle (l) is one inch less than five times it's width;

`\longrightarrow` l = (5w - 1) in

Perimeter of rectangle = 46 inches

Formula of perimeter of rectangle = 2(Length + Width)

So,

`\rm \implies 2(Length + Width) = 46 \\ \\ \rm \implies 2(5w - 1 + w) = 46 \\ \\ \rm \implies 2(6w - 1) = 46 \\ \\ \rm \implies 6w - 1 = (46)/(2) \rm \implies 6w - 1 = 23 \\ \\ \rm \implies 6w = 23 + 1 \\ \\ \rm \implies 6w = 24 \\ \\ \rm \implies w = (24)/(6) \\ \\ \rm \implies w = 4 \: in`

`\therefore` Width of the rectangle (w) = 4 in

Length of rectangle (l) = 5 × 4 - 1 = 19 in