# A rectangular room has an area of 400 square foot. The length is 7 feet less than twice the width. How do you find the dimensions of the room?

Apr 9, 2018

$400 = w \times \left(2 w - 7\right)$. Length is 25 ft and width is 16 ft.

#### Explanation:

You can put an equation to solve the problem:

$A = w \times l$

where l is $2 w - 7$

Now you can solve the question.

$400 = 2 {w}^{2} - 7 w$

w will be 16 feet.

I used trial and error method to find w. If you want, you can use quadratic formula to solve the question. If w is 16 ft,

$400 = \left(2 \times {16}^{2}\right) - \left(7 \times 16\right)$

$400 = 512 - 112$

It satisfies the equation.

Length is 25 ft and width is 16 ft.