The area of a rectangular wall of a barn is 28 square feet.i its length is 10 feet longer than twice its width . Find the length and width of the wall of the barn

Answer 1

width=w

length=10+2w

w(10 +2w) =28

10w +2w squared = 28

2w squared +10 w - 28 =0

factor this trinomia;

2(w squared + 5w-14)=0

2(w+7)(w-2)=0

w+7=0

w=-7----width can not be negative

w-2=0

w=2 which is the answer

l = 14

Answer 2

The second sentence of the problem gives the length in terms of the width. Let W = the width and let L = the length of the wall, in feet. Then the second sentence says that

L= 2W +10 (ten feet longer than twice the width)

The area of the wall A = W * L = W * (2W + 10). This is given as 28 square feet, so

28 = W * (2W + 10) = 2W^2 + 10W

To simplify, first divide both sides by 2 to get 14 = W^2 + 5W

Subtract 14 from both sides to get the quadratic equation

0 = W^2 + 5W - 14

Factor to get 0 = (W+7)*(W-2)

Therefore, either 0= W+ 7, so W = -7, or 0= W-2, so W=2

Since a width cannot be a negative number, W=2 feet. Plug into the expression for length to get

L= 2(2) + 10, or L = 14 feet

Answer 3

w represents the width

2w + 10 represents the length

w(2w + 10) = 28

Can you solve for w and answer?

Answer 4

Hello Destinee,

Let w be the width of the rectangular wall. Since the problem indicates that the length is 10 feet longer than twice the width, we can express the length in terms of the width w as follows:

Length = 2w + 10.

Now using the fact that the area is 28 square feet, we have

(Length)(Width) = 28,

which gives the equation

(2w + 10)w = 28.

Thus,

2w² + 10w = 28

2w² + 10w - 28 = 0

We can simplify this equation by dividing both sides by 2, then solve the equation by factoring.

w² + 5w - 14 = 0

(w + 7)(w - 2) = 0, which gives

w = -7 or w = 2.

Since the width of the rectangle cannot be negative, we have w = 2. From this, we can obtain the length.

Length = 2w + 10 = 2(2) + 10 = 14.

Therefore, the dimensions of the rectangular wall are

length = 14 feet and width = 2 feet.

Hope that helps! Let me know if you need any clarification.

William.