Rectangle perimeter question

Question

Question 1: The length of a rectangle is 3 times it’s width. What is it’s width if it’s perimeter is 120 centimeters?

Question 2: The length of a rectangle is 3 centimeters more than it’s width. What is it’s width if it’s perimeter is 120 centimeters?

Answer 1

Question 1: The length of a rectangle is 3 times its width. What is its width if its perimeter is 120 centimeters?

Start off by labeling your sides as (l) and (w). Then think of the perimeter formula: 2l+2w=p

Given that the length is equal to 3 times the width, we can say that l=3w.

Substitute in 3w for l in the perimeter formula: 2(3w) + 2w = p and simplify: 6w+2w=p so 8w=p

Given that the perimeter is 120, you can write the equation as 8w=120.

Then just solve for w. 120÷8 = 15. So the width is 15 and the length is 45.

Question 2: The length of a rectangle is 3 centimeters more than its width. What is its width if its perimeter is 120 centimeters?

Given that the length is 3 cm more than the width, we can say that l = w + 3.

Substitute that into your equation: 2(w+3) + 2w = 120 and simplify.

2w+6+2w=120

4w + 6 = 120

Subtract 6 from both sides

4w = 114

Divide both sides by 4.

w = 28.5

Its width is 28.5 cm and its length is 31.5 cm

Answer 2

So let's start by labeling our variables:

length = L

width = W

If we know that the length of a rectangle is 3 times the width, we can make this equation below:

L = 3W

Okay, now that we have an equation relating length and width, let's continue with the problem. It seems we have to solve for the width (W) if the perimeter is 120. The perimeter is defined as the total side length of the rectangle. There are 4 sides to a rectangle. Two of them have the same length (L), and the other two have the same length (W).

So, we can define the perimeter of the rectangle with the equation below:

perimeter = 2L + 2W

If we know the perimeter is 120, we can make the equation below:

120 = 2L + 2W

Now, since we have already created the equation relating length and width, (L = 3W), let's substitute it into the perimeter equation.

120 = 2(3W) + 2W = 6W + 2W = 8W

If 8W = 120, W = 120/8 = 15.

Now that we have solved part 1, let's continue to part 2. It is actually going to be the same exact method I used for part 1. Try to solve it yourself first.

Our new length and width relation equation is L = 3 + W because the length is 3 more than the width. Let's plug this into the perimeter equation we made for part 1.

120 = 2L + 2W = 2(3 + W) + 2W= (6 + 2W) + 2W = 6 + 4W

Now that we have 120 = 6 + 4W, we can say that 120 - 6 = 4W if we subtract 6 from both sides.

Let's divide both sides by 4 and we get W = 28.5

Hope this helped

-Nitish