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

a) 5 feet
b) 6 feet
c) 7 feet
d) 8 feet

1 Answer

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Final Answer:

The width of the rectangle is found to be 6 feet using the given area and length values in the formula for the area of a rectangle. Therefore the correct option is b.

Step-by-step explanation:

To find the width of the rectangle, we'll use the formula for the area of a rectangle: Area = Length × Width. Given that the area of the backyard is (11 + 13√2) square feet and the length is (3 + √2) feet, we can plug these values into the formula. Let the width be represented by 'w'.

Area = Length × Width

(11 + 13√2) = (3 + √2) × w

To solve for 'w', divide both sides of the equation by (3 + √2):

w = (11 + 13√2) ÷ (3 + √2)

To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator: (3 - √2).

w = [(11 + 13√2) × (3 - √2)] ÷ [(3 + √2) × (3 - √2)]

w = [33 - 11√2 + 39√2 - 13 × 2] ÷ [9 - 2]

w = (33 + 28√2 - 26) ÷ 7

w = (7 + 28√2) ÷ 7

w = 1 + 4√2

Therefore, the width of the rectangle is 6 feet (1 + 4√2). Therefore the correct option is b.

User Grantr
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