Question

The area of a rectangular wall of a barn is 216 square feet. Its length is 6 feet longer than twice its width. Find the length and width of the wall of the barn

Answer 1

Answer:

Length is 24 feet and width is 9 feet.

Step-by-step explanation:

It is given that length of a rectangular wall is 6 feet longer than twice its width.

Let x feet be the width of wall.

Length = 2x+6 feet

Area of rectangle is

$A=length \times width$

$A=(2x+6)\times x$

$A=2x^2+6x$

It is given that area of a rectangular wall of a barn is 216 square feet.

$2x^2+6x=216$

$x^2+3x=108$

$x^2+3x-108=0$

Splitting the middle term, we get

$x^2+12x-9x-108=0$

$x(x+12)-9(x+12)=0$

$(x+12)(x-9)$

$x=-12,9$

Width can not be negative. So width is 9 feet.

Length $=2(9)+6=18+6=24\text{ feet}$

Therefore, length is 24 feet and width is 9 feet.