The area of a rectangular wall of a barn is 144 square feet. It’s length is 12 feet longer than twice it’s width. Find the length and width of the wall of the barn.

Answer 1

Hi Holly,

I solved by completing the square. Area=L x W

in this case : 144= (2w+12)x w

Let's switch sides for convenience: 2w² + 12w = 144

Now divide each term by 2 w² +6w = 72

Now take half of the middle term and square it w² + 6w +9=72+9

The completed sq is (w+3)²= 81 Take root of both sides w+3 = 9 w=6

If width is 6 then Length is 2x6+12= 24 Check: 24 x6= 144 sq ft

Hope you see! enjoy!

Answer 2

Greetings! Lets solve this shall we ?

Let the Area be A = l * w = (2x+12)(x) = 144. We must solve for x to figure out what the length and width.

Then (2x+12)(x) = 144

2x²+12x - 144 = 0

2(x²+6x-72) = 0

x²+6x-72 = 0

(x+12)(x-6) = 0

x = -12 and 6..................We cannot have a negative width or negative length so we must get rid of -12 and use x = 6.

Then, the length is l = 2x + 12 and the width is just x.

Hence, the width is x = 6 feet and the length is 2(6)+12) = 24 feet!

I hope this helps!