Question

The length of a rectangle is 3 centimeters less than five times its width. Its area is 14 square centimeters. Find the dimensions of the rectangle.

Find the Width and the Length
W=
L=​

Answer 1

The length of rectangle is 7 cm and width is 2 cm.

Explanation:

Given that:

Area of rectangle = 14 square centimeters

The length of a rectangle is 3 centimeters less than five times its width.

Let,

L be the length and W be the width of the rectangle.

L = 5W - 3

Area of rectangle = Length * Width

14 = (5W-3)*W

`14=5W^2-3W\\5W^2-3W-14=0`

Factorizing the equation;

`5W^2-10W+7W-14=0\\5W(W-2)+7(W-2)=0\\(5W+7)(W-2)=0`

Either,

5W+7 = 0

5W = -7

W = -7/5

Or,

W-2 = 0

W=2

As width of rectangle cannot be negative, therefore,

Width = 2 centimeters

Length = 5(2) -3 = 10-3 = 7

Hence,

The length of rectangle is 7 cm and width is 2 cm.