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# If the lengths of the legs of a right triangle are integers, what is

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Re: If the lengths of the legs of a right triangle are integers, what is [#permalink]
gmatt1476 wrote:
If the lengths of the legs of a right triangle are integers, what is the area of the triangular region?

(1) The length of one leg is 3/4 the length of the other.
(2) The length of the hypotenuse is 5.

The triangle is a right triangle, so it must abide by the rules of Pythagorean's theorem: $$a^2$$ + $$b^2$$ = $$c^2$$

(1) There are an infinite amount of Pythagorean triples that have one leg equal to 3/4 of the other.

Side lengths could be: 3,4,5...... 6,8,10......9,12,15......12,16,20......etc

Not Sufficient

(2) The only right triangle that has a hypotnuse of 5, with all sides being integers, is the 3,4,5 Pythagorean triple.

Sufficient
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Re: If the lengths of the legs of a right triangle are integers, what is [#permalink]
If the lengths of the legs of a right triangle are integers, what is the area of the triangular region?

(1) The length of one leg is 3/4 the length of the other.

Many values fit this scenario; INSUFFICIENT.

(2) The length of the hypotenuse is 5.

Since we're told the lengths of the legs are integers, this legs must be 3 and 4. SUFFICIENT.

Note that if the question did not state that the legs were integers, the answer would then be E.
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Re: If the lengths of the legs of a right triangle are integers, what is [#permalink]
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Re: If the lengths of the legs of a right triangle are integers, what is [#permalink]
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