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The area of a rectangle wall of a barn is 234 square feet. It's length is 8 feet longer than twice its width. Find the length and width of the wall of the barn.

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EGaddIndustries
First:
Area=length•width

Now, we know that the area is 234 & the length is 8 feet longer than twice its width. So, if width is w:
234 = w(2w+8)
Now, simplify:
234=2w^2+8w
This is starting to look like a quadratic:
0=2w^2+8w-234
0=w^2+4w-117
Factor it out:
0=(w+13)(w-9)
So w=9, -13
Now, since we're dealing with the real world, we'll say w=9 (because you can't have negative distance).
So, our width is 9 feet.
234=9(18+8)
234=9(26)
And so the length is 26 feet:
26x9 feet

Hope this helps!
varshamittal029

The length of the wall is : 26 ft.

 and width of the wall is: 9 ft.

What is area of a rectangle?

The shape/polygon of a rectangle is two dimensional, having four sides, four vertices, and four right angles. The rectangle's two opposing sides are equal and parallel to one another. The space a rectangle occupies is known as its area. The area of a rectangle can also be defined as the region inside its border.

The area of a rectangle is: Area= length × width

Solution:

area = 234

length = ?

width = ?

Given, length is 8 ft greater than twice the width.

Now, l = 2w ₊ 8

        l × w = 234 (given)

Substitute for l

(2w ₊ 8)w = 234

multiply

2w² ₊ 8w = 234

2w² ₊ 8w ₋ 234 = 0

Now divide by 2 to eliminate the coefficients of w.

w² ₊ 4w ₋ 117=0

get the factors for the above equation.

We get the factors as: 9 and ₋13,( ₋13 is not applicable as width cannot be negative)

Hence we get the width as 9, now substitute it in:

l = 2w ₊ 8

l = 2(9) ₊ 8

l = 26 ft,

Hence the length and width of the rectangle is 26 ft and 9 ft respectively.

Learn more about "Rectangles" here-

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