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# A right triangle has sides of lengths A and 2B and hypotenuse of lengt

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Joined: 02 Sep 2009
Posts: 52279
A right triangle has sides of lengths A and 2B and hypotenuse of lengt  [#permalink]

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21 Dec 2018, 01:20
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55% (hard)

Question Stats:

56% (01:14) correct 44% (01:15) wrong based on 36 sessions

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A right triangle has sides of lengths A and 2B and hypotenuse of length A + B. What is the perimeter?

(1) A = 3
(2) A = 3B/2

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Re: A right triangle has sides of lengths A and 2B and hypotenuse of lengt  [#permalink]

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21 Dec 2018, 01:41
Given that sides of a right angle triangle are of lengths A and 2B, and the hypotenuse is of length A + B.
Accordingly to Pythagoras theorem, (A + B)^2 = A^2 + (2B)^2
Solving the above equation we get 3B^2 - 2AB = 0
Solving the quadratic equation, B(3B - 2A) = 0
Either B = 0 (this is not a possible position because if B is zero, one of the side length of triangle become 0)
Or 3B = 2A

We have to find the perimeter, i.e. 2A + 3B

Statement 1. A = 3 is sufficient to solve the question
We already know 3B = 2A
Therefore, B = 2
So, Perimeter 2A + 3B = 12

Statement 2. A = 3B/2 is NOT sufficient to solve the question
Statement 2 can be derived directly from the question and hence do not add any new information.

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A right triangle has sides of lengths A and 2B and hypotenuse of lengt  [#permalink]

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21 Dec 2018, 05:05
3

Solution

Given:
• Lengths of two sides of a right triangle = A and 2B
• Length of hypotenuse of the triangle = A + B

To find:
• The perimeter of the triangle

Approach & Working
• $$A^2 + (2B)^2 = (A + B)^2$$
• $$A^2 + 4B^2 = A^2 + B^2 + 2AB$$
• $$3B^2 = 2AB$$
• Thus, 3B = 2A

Perimeter of the triangle = A + 2B + A + B = 2A + 3B = 2A + 2A = 4A

Thus, if we know the value of either A or B we can find the perimeter of the right triangle

Analysing Statement 1
“A = 3”
Therefore, Statement 1 is sufficient

Analysing Statement 2
“A = 3B/2”
• This does not give the value of A or B

Therefore, Statement 2 is not sufficient

Hence, the correct answer is Option A.

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A right triangle has sides of lengths A and 2B and hypotenuse of lengt &nbs [#permalink] 21 Dec 2018, 05:05
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