Question

The area of a rectangular wall of a barn is 260 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:

l = 26, w = 10

Step-by-step explanation:

These types of word problems always want you to use variables to find the answer. Variables are always going to represent the numbers you don't know.

This question wants you to find the length and width of the wall of the barn, so let's just use l for length (let l = length of barn wall) and w for width (let w = width of barn wall); this is called defining your variables, so that you--or anyone who looks at your work--know what the letter variable represents.

Now we use the other information we have to find what values the variables actually equal.

We know that the length is 6 feet longer than twice the width. To express this in terms of numbers and variables: l = 6 + 2w. This makes sense, right?

length = 6 + (2 * width)

If the total area of the wall is 260 square feet and we need to find the length and width, we can use the A = lw formula, which you can use for any rectangle. Since 260 is the area (A), we can put that into the formula so that we have 260 = lw.

Next, use the expression we came up with earlier (l = 6 + 2w) to help find the answer.

We have two equations now (l = 6 + 2w and 260 = lw) and we just need to put them together.

This part is the same as solving any other linear equation.

The approach I'll use is substitution:

l = 6 + 2w

260 = lw

Substitute 6 + 2w in for l:

260 = (6 + 2w) w

Distribute:

260 = 6w + 2w²

Solve:

w² + 3w - 130 = 0

w = -13, w = 10

(The width of a rectangle cannot be negative, so it has to be 10 ft.)

We're almost there. The last thing to do is to find the length. Just plug in 10 for w in the l = 6 + 2w formula:

l = 6 + 2(10) = 6 + 20 = 26

To check your work, we can double the width and add 6 to get 26, and 26 * 10 is 260.

So, the length of the wall of the barn is 26 and the width of the wall of the barn is 10.