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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
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?
A. 30
B. 40
C. 50
D. 60
E. 70
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A. 30
B. 40
C. 50
D. 60
E. 70
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE GEOMETRY
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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
25 Jul 2023, 10:08
Expert Reply
OE
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)
_________________
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)
_________________
gmatclubot
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