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The area of a backyard in the shape of a rectangle is (11 + 13√2) square feet. If the length measures (3 + √2) feet, find the width of the rectangle.

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Final answer:

The width of the rectangle is (59 + 50√2) / (3 + √2) feet.

Step-by-step explanation:

The area of a rectangle is given by the formula length x width. In this case, the area is given as (11 + 13√2) square feet, and the length is given as (3 + √2) feet. To find the width, we can rearrange the formula to solve for width: width = area / length. Substituting the given values, we get:

width = [(11 + 13√2) square feet] / [(3 + √2) feet]

To make the calculation easier, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator. Simplifying the expression gives us:

width = (11 + 13√2) / (3 + √2) feet

Using the distributive property, we get:

width = [11(3) + 11(√2) + 13(√2)(3) + 13(√2)(√2)] / (3 + √2) feet

Simplifying further gives:

width = (33 + 11√2 + 39√2 + 26) / (3 + √2) feet

Combining like terms gives:

width = (59 + 50√2) / (3 + √2) feet

This is the exact value for the width of the rectangle. If you need a decimal approximation, you can use a calculator to divide the numerator by the denominator. Hope this helps!

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