Question

The length of a rectangle is 4.6 feet more than the width. The perimeter is 38 feet. This situation can be represented with the system L-w=4.6 and 2L +2w = 38, where L represents the length of the rectangle and w represents the width. Find the demensions of the rectangle. Express your answers as decimals if recessary.
The width is________ feet, and the length is________ feet.

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Answer 1

Answer:

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Answer 2

The width is 7.2 feet, and the length is 11.8 feet.

We have the system of equations:

L - w = 4.6 (equation 1)

2L + 2w = 38 (equation 2)

In equation 1, we can solve for one variable in terms of the other:

L = w + 4.6

Substituting this into equation 2, we get:

2(w + 4.6) + 2w = 38

Simplifying:

2w + 9.2 + 2w = 38

4w + 9.2 = 38

4w = 28.8

w = 7.2

So the width is 7.2 feet. When we substitute this for L in our expression, we obtain:

L = 7.2 + 4.6 = 11.8

So the length is 11.8 feet.

Therefore, the width is 7.2 feet, and the length is 11.8 feet.

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