Solve application problems using linear equations.

Question

A rectangular room is 1.7 times as long as it is wide, and its perimeter is 28 meters. Find the dimensions of the room.

Answer 1

A rectangular room is 1.7 times as long as it is wide, and its perimeter is 28 meters. Find the dimensions of the room.

Let w = the room's width.

Let l = length.

Let p = perimeter

The formula for the perimeter of a rectangle is:

w + w + l + l = p or 2w + 2l = p

We are given the perimeter as 28 meters so:

2w + 2l = 28

Since the length of the room is 1.7 times as long as it's width, the length (l) = 1.7w

2w + 2(1.7w) = 28

Now that we have our equation we can solve for w.

1. Multiply 2(1.7w) = 2 * 1.7 * w: w = 3.4w
2. Substitute 3.4w for 2(1.7w): 2w + 3.4w = 28
3. Add 2w + 3.4w: 5.4w = 28
4. Divide 28 / 5.4 = 5.18 (round to 5.2)
5. The width equals 5.2 meters.
6. Multiply w * 1.7 to get the length: l = 8.84 (round to 8.8)
7. The dimensions of the room are 5.2 meters wide by 8.8 meters long or 5.2 by 8.8.

Check: (2)5.2 * (2)8.8 = 28

1. Multiply (2)5.2 * (2)8.8: 10.4 * 17.6 = 28
2. Add 10.4 * 17.6: 28 = 28

Answer 2

1. L = 1.7W
2. 28 = 2L +2W
3. 28 = 2(1.7W) +2W
4. 28 = 3.4W + 2W
5. 28 = 5.4W
6. W = 5.2
7. L = 1.7 (5.2) = 8.8
8. So the Dimensions are 8.8 x 5.2
9. Verify the perimeter is 8.8 + 8.8 + 5.2 + 5.2 = 28