Question

A rectangle has a length 10 m less than twice its width. When 2 m are added to the​ width, the resulting figure is a square with an area of 196 m squared. Find the dimensions of the original rectangle.

Answer 1

The length of the original rectangle is 14 meters and the width of the original rectangle is 12 meters

Explanation:

Let

l ----> the length of the original rectangle

w ----> the width of the original rectangle

we know that

`l=2w-10` ----> equation A

`196=(w+2)^(2)` ----> area of a square

Solve for w

square root both sides

`(w+2)=(+/-)14`

`w=14=(+/-)14-2`

`w=14=14-2=12\ m`

`w=14=-14-2=16\ m` -----> this solution not make sense

so

`w=12\ m`

Find the value of L

`l=2(12)-10=14\ m`

therefore

The length of the original rectangle is 14 meters and the width is 12 meters