Question

A rectangular garden has length twice as great as its width. A second rectangular garden has the same width as the first garden and length that is 4 meters greater than the length of the first garden. The second garden has area of 70 square meters.
What is the width of the two gardens?

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m

Answer 1

Use the information to write the dimensions of each rectangle in terms of w, the width of the 1st one.

1st rectangle;
l = 2w
w = 2

2nd rectangle:
w = w 
l = 2w + 4

If the area of the 2nd rectangle is 70 square meters, you will use the area formula to write an equation that you will solve using the factoring.

A = lw
70 = w(2w + 4)
70 = 2w^2 + 4w
0 = 2w^2 + 4w -70
0 = 2 (w^2 +2w - 35)
0 = 2 (w + 7) (w - 5)

To get zero, the width would need to be -7 or 5.  Because it is a distance, it has to be 5 meters.

The width of both rectangles is 5 meters.