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A flat garden in the shape of right angled triangle has the area 600 s
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21 Jun 2023, 03:18
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A flat garden in the shape of right angled triangle has the area 600 square feet, is bounded by fence on two of its sides and a walkway on the longest side. If the entire length of the fence is 70 feet. What is the length in feet of the walkway?
Re: A flat garden in the shape of right angled triangle has the area 600 s
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25 Jul 2023, 10:08
Expert Reply
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Consider the triangle ABC, right angled at B. Here, the longest side is AC. So, the walkway is across AC and fence is across AB and BC. Now, AB + BC = 70 If AB = x, then AC = (70 - x) Area of ∆ ABC = ½ × AB × AC 600 = ½ × x × (70 – x) 1200 = 70x - 𝑥^2
𝑥^2 − 70𝑥 + 1200 = 0 x = 40 or 30. So, AB and BC are either 30 or 40. Using Pythagoras theorem, we get AC = 50. Ans. (C)
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