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!