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# What is the area of the right triangle shown?

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Math Expert
Joined: 02 Sep 2009
Posts: 44566
What is the area of the right triangle shown? [#permalink]

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26 Mar 2018, 23:00
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Difficulty:

55% (hard)

Question Stats:

85% (00:44) correct 15% (01:15) wrong based on 46 sessions

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What is the area of the right triangle shown?

(1) a + b =14
(2) c^2 = a^2 + 36

[Reveal] Spoiler:
Attachment:

2018-03-27_0957.png [ 9.32 KiB | Viewed 421 times ]
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 44566
Re: What is the area of the right triangle shown? [#permalink]

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26 Mar 2018, 23:06
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Bunuel wrote:

What is the area of the right triangle shown?

(1) a + b =14
(2) c^2 = a^2 + 36

[Reveal] Spoiler:
Attachment:
2018-03-27_0957.png

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Re: What is the area of the right triangle shown? [#permalink]

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27 Mar 2018, 00:57
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KUDOS
Bunuel wrote:

What is the area of the right triangle shown?

(1) a + b =14
(2) c^2 = a^2 + 36

[Reveal] Spoiler:
Attachment:
2018-03-27_0957.png

To determine the Area, we need to uniquely determine a & b sides of the triangle.

(1) Sum of the sides is known but each side is not. Insufficient.

(2) $$c^2 = a^2 + 36$$ on comparing with the Pythagoras theorem for this triangle:$$b^2 = 36$$ or $$b = 6$$ However, we do not know a. Insuff

(1) + (2) : we know b from (2) and we can find a as (1) gives us the sum of a & b. Sufficient!

Hence Option (C) is correct.

Best,
Re: What is the area of the right triangle shown?   [#permalink] 27 Mar 2018, 00:57
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