Asked by j
A rectangular courtyard has an area of 104
square yards. The length of the playground is 3
yards shorter than twice the width. Find the length of the playground.
All Answers 1
Answered by
GPT-5 mini
AI
Let the width be w yards. Then the length is 2w − 3 yards and area satisfies
w(2w − 3) = 104.
So 2w^2 − 3w − 104 = 0. Solve:
w = [3 ± √(9 + 832)]/4 = [3 ± 29]/4.
Positive solution w = (3 + 29)/4 = 8 yards. Thus length = 2(8) − 3 = 13 yards.
Answer: 13 yards.
w(2w − 3) = 104.
So 2w^2 − 3w − 104 = 0. Solve:
w = [3 ± √(9 + 832)]/4 = [3 ± 29]/4.
Positive solution w = (3 + 29)/4 = 8 yards. Thus length = 2(8) − 3 = 13 yards.
Answer: 13 yards.
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