Question

The length of a rectangle is 5 inches less than 3 times the width. The perimeter is 70 inches. Find the length and the width.

The length is __ inches and the width is __ inches.

Answer 1

Length of the Rectangle = 10 inches

and Width = 25 inches

Explanation:

Let the width of the rectangle = k inches

So, the Length of the rectangle = (3k - 5) inches

Perimeter = 70 inches

Now, Perimeter of the Rectangle = 2(Length + Width)

= 2 (k + (3k-5))

⇒ 2 (k + (3k-5)) = 70

or, 2(k + 3k -5) = 70 ⇒ 2(4k - 5) = 70

⇒ 8k - 10 = 70

or, 8k = 70+ 10 = 80

or, k = 80/8 = 10

So, the Length = 10 inches

Hence, Width = 3k - 5 = 3(10) - 5 = 30 - 5 = 25 inches

So, Length of the Rectangle = 10 inches

and Width = 25 inches