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

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

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New post Updated on: 12 Mar 2013, 05:21
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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, 05:13.
Last edited by Bunuel on 12 Mar 2013, 05:21, edited 1 time in total.
Edited the question.
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Re: The sides of right triangle ABC are such that the length of  [#permalink]

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New post 12 Mar 2013, 05:29
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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.

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

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New post 22 Nov 2015, 18:20
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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


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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New post 10 May 2016, 21:20
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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New post 11 May 2016, 01:55
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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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Re: The sides of right triangle ABC are such that the length of &nbs [#permalink] 22 Sep 2018, 01:25
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