Help with algebra

Question

The length of a rectangle is six times its width. if the perimeter is 112 m find its length and width

Answer 1

I have solved this word problems step-by-step in the attached video. Check it out and let me know if you have any additional questions. I hope you find this solution to be helpful. Take care!

-Dr. Christal-Joy Turner

Answer 2

The perimeter of a rectangle is the sum of the measures of its sides. So, if L is the length and W is the width of the rectangle, we have

112 = 2L + 2W.

Now, we're told the length is 6 times the width of the rectangle; that is, L = 6W. If we substitute this into our previous equation, we get

112 = 2(6W) + 2W = 12W + 2W = 14W.

Now we have an equation with only one variable, and we can solve 112 = 14W for W by dividing each side by 14 to figure out W:

W = 8.

Lastly, we recall L = 6W, so L = 6(8) = 48.

L = 48,

W = 8.

We can confirm by checking P = 2(48) + 2(8) = 112. Nice! :)

Answer 3

Hi Kristina,

The perimeter of a rectangle has the formula: P = 2(l + w)

You're told that: P = 112 and l = 6w, so let's use that information and plug it in the perimeter formula:

112 = 2(6w + w)

Divide both sides by 2: 56 = 6w + w

Add the w's on the right side: 56 = 7w

Divide both sides by 7: 8 = w

So the width is w = 8 meters

Remember the length is six times the width: l = 6 x 8 = 48 meters

Let's check our answers: perimeter P = 2(48 +8) = 2(56) = 112 which is the perimeter given in the problem, so the answers are correct!

Final answers: the length is 48 meters, the width is 8 meters.