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The sides of right triangle ABC are such that the length of

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Joined: 09 Feb 2013
Posts: 114
The sides of right triangle ABC are such that the length of  [#permalink]

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Updated on: 12 Mar 2013, 04:21
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Question Stats:

69% (02:36) correct 31% (02:54) wrong based on 183 sessions

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The sides of right triangle ABC are such that the length of side AB is greater than the length of side BC, which itself is greater than the length of side AC. If side AB = 143 and side AC = 55, what is the area of the triangle?

A. 3113
B. 3224
C. 3432
D. 3630
E. 7260

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Originally posted by emmak on 12 Mar 2013, 04:13.
Last edited by Bunuel on 12 Mar 2013, 04:21, edited 1 time in total.
Edited the question.
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Joined: 02 Sep 2009
Posts: 52432
Re: The sides of right triangle ABC are such that the length of  [#permalink]

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12 Mar 2013, 04:29
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emmak wrote:
The sides of right triangle ABC are such that the length of side AB is greater than the length of side BC, which itself is greater than the length of side AC. If side AB = 143 and side AC = 55, what is the area of the triangle?

A. 3113
B. 3224
C. 3432
D. 3630
E. 7260

Given that AB>BC>AC. So, AB is the hypotenuse of the triangle.

$$BC=\sqrt{143^2-55^2}=\sqrt{(11*13)^2-(11*5)^2}=11\sqrt{13^2-5^2}=11*12$$.

The area = 1/2*BC*AC = 1/2*(11*12)*55 = 66*55 = 3630.

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Re: The sides of right triangle ABC are such that the length of  [#permalink]

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22 Nov 2015, 17:20
4
emmak wrote:
The sides of right triangle ABC are such that the length of side AB is greater than the length of side BC, which itself is greater than the length of side AC. If side AB = 143 and side AC = 55, what is the area of the triangle?

A. 3113
B. 3224
C. 3432
D. 3630
E. 7260

Bunuel's solution is exactly how I would have answered this question.
However, if I had no idea how to answer the question (or if I had only 10 seconds remaining), I still would have guessed D.

Here's why:
Notice that E (7260) is twice as big as D (3630).
Since area of a triangle = ONE-HALF times base times height, answer choice E is a good distractor for people who forget to HALVE the product of the base and height.
So, I'd GUESS D.

Cheers,
Brent
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Re: The sides of right triangle ABC are such that the length of  [#permalink]

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10 May 2016, 20:20
There is a special property for a right triangle which is valid here 5k:12k:13k
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The sides of right triangle ABC are such that the length of  [#permalink]

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11 May 2016, 00:55
1
According to right angle property: sides ratio 5x:12x:13x

Here AC>BC>AB
13>12>5

Here AC =143= 13*11 so X=11 BC=12*11

Area= .5*AB*BC
= .5*55*12*11=3630
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Re: The sides of right triangle ABC are such that the length of  [#permalink]

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22 Sep 2018, 00:25
Hello from the GMAT Club BumpBot!

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Re: The sides of right triangle ABC are such that the length of &nbs [#permalink] 22 Sep 2018, 00:25
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