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. W= L=​

Answer 1

Explanation:

Let breadth =x

Length=5x-3

As we know that in a rectangle

`\boxed{\sf Area=lb}`

• Substitute the values

`{:}\hookrightarrow\sf x (5x-3)=14`

`{:}\hookrightarrow\sf 5x^2-3x=14`

`{:}\hookrightarrow\sf 5x^2-3x-14=0`

`{:}\hookrightarrow\sf 5x^2-10x+7x-14=0`

`{:}\hookrightarrow\sf 5x (x-2)+7 (x-2)=0`

`{:}\hookrightarrow\sf (x-2)(5x+7)=0`

`{:}\hookrightarrow\sf x-2=0\quad or\quad 5x+7=0`

`{:}\hookrightarrow\sf x=2\:or\:x=\frac {-7}{5}`

• Ignore negative value

`{:}\hookrightarrow\sf Breadth =2cm`

`{:}\hookrightarrow\sf Length=5 (2)-3=10-3=7cm`