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

Answer:

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

Step-by-step 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