Question

The length of a rectangle is three times its width. The perimeter of the rectangle is 100 inches. What are the dimensions of the rectangle?

Answer 1

The width of the rectangle is 12.5 inches, and the length is three times the width, which calculates to 37.5 inches. These dimensions satisfy the given perimeter of 100 inches.

Step-by-step explanation:

Finding the Dimensions of a Rectangle Given its Perimeter

A student has asked about finding the length and width of a rectangle where the length is three times its width and the perimeter is 100 inches. To solve this, we can set up two equations based on the given information. Let's denote the width of the rectangle as w and the length as 3w.

The formula for the perimeter P of a rectangle is P = 2l + 2w, where l is the length and w is the width. Substituting l with 3w (since length is three times the width), and P with 100 inches, we get:

100 = 2(3w) + 2w.

This simplifies to: 100 = 6w + 2w, which further simplifies to 100 = 8w. Dividing both sides by 8, we find that w = 12.5. Therefore, the dimensions of the rectangle are: width = 12.5 inches and length = 3(12.5) = 37.5 inches.

Answer 2

The dimensions are 12.5 inches width and 37.5 inches length.

Step-by-step explanation:

Givens:

• Length is three times the width, this can be represented as:
  `l=3w`
• The perimeter is 100 inches. The perimeter is expressed as:
  `P=2(l+w)`

So, to find the dimensions of the rectangle, that is, the length and width, we have to replace the first equation into the second one:

`100=2(3w+w)\\(100)/(2)=4w\\w=(100)/(8)= 12.5 \ in`

The length can be found using the first expression:

`l=3(12.5)=37.5`

Therefore, the dimensions are 12.5 inches width and 37.5 inches length.