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The sides of a right-angled triangle are n, 2n1, 2n+1. What is the l
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09 Feb 2025, 12:02
09 Feb 2025, 12:02
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The sides of a right-angled triangle are \(n, 2n–1, 2n+1\). What is the length of the hypotenuse, if n is a positive integer?
A. 8
B. 12
C. 15
D. 17
E. 18
A. 8
B. 12
C. 15
D. 17
E. 18
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Re: The sides of a right-angled triangle are n, 2n1, 2n+1. What is the l
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08 Mar 2025, 00:51
08 Mar 2025, 00:51
Expert Reply
The three sides of a right angle triangle are given as $\(n, 2 n-1 \& 2 n+1\)$
As n is a positive integer, the greatest of the three sides i.e. hypotenuse must be $\(2 \mathrm{n}+1\)$
Now, applying Pythagoras theorem i.e. Hypotenuse $\({ }^2=\)$ Perpendicular $\(^2+\)$ Base $^2$ in the triangle we get $\((2 n+1)^2=(2 n-1)^2+(n)^2\)$ which when simplified gives $\(n^2-8 n=0 \Rightarrow n=0$ or $n=8\)$
The value of $n$ cannot be zero, so it has to be 8 .
Thus, the length of the hypotenuse $\(=2 n+1=2 \times 8+1=17\)$.
Hence the answer is (D).
As n is a positive integer, the greatest of the three sides i.e. hypotenuse must be $\(2 \mathrm{n}+1\)$
Now, applying Pythagoras theorem i.e. Hypotenuse $\({ }^2=\)$ Perpendicular $\(^2+\)$ Base $^2$ in the triangle we get $\((2 n+1)^2=(2 n-1)^2+(n)^2\)$ which when simplified gives $\(n^2-8 n=0 \Rightarrow n=0$ or $n=8\)$
The value of $n$ cannot be zero, so it has to be 8 .
Thus, the length of the hypotenuse $\(=2 n+1=2 \times 8+1=17\)$.
Hence the answer is (D).
gmatclubot
Re: The sides of a right-angled triangle are n, 2n1, 2n+1. What is the l [#permalink]
08 Mar 2025, 00:51
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