Question

Find the dimensions of a rectangular room that is three feet shorter than its length, with a perimeter of 42 feet. a) Length = 18 feet, Width = 12 feet b) Length = 15 feet, Width = 12 feet c) Length = 14 feet, Width = 11 feet d) Length = 21 feet, Width = 15 fee

Answer 1

Let's use algebra to solve this problem. Let L represent the length of the room and W represent the width.

We know that the room is three feet shorter than its length, so we can write:

W = L - 3

The perimeter of a rectangular room is given by the formula:

Perimeter = 2L + 2W

Given that the perimeter is 42 feet, we can write:

42 = 2L + 2(L - 3)

Now, let's solve for L:

42 = 2L + 2L - 6

42 = 4L - 6

Add 6 to both sides:

48 = 4L

Divide by 4 to find the length:

L = 48 / 4

L = 12 feet

Now that we have the length, we can find the width using W = L - 3:

W = 12 - 3

W = 9 feet

So, the dimensions of the rectangular room are:

Length = 12 feet

Width = 9 feet

Therefore, the correct answer is not among the options provided.