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# If a right triangle has legs

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If a right triangle has legs [#permalink]  14 Nov 2017, 08:12
Expert's post
00:00

Difficulty:

5% (low)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

If a right triangle has legs of 20 cm and 21 cm, what is the length of the hypotenuse?

A. \sqrt{41} cm

B. 20.5 cm

C. 29 cm

D 41 cm

E. 45 cm
[Reveal] Spoiler: OA

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Re: If a right triangle has legs [#permalink]  14 Nov 2017, 08:51
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Carcass wrote:

If a right triangle has legs of 20 cm and 21 cm, what is the length of the hypotenuse?

A. \sqrt{41} cm

B. 20.5 cm

C. 29 cm

D 41 cm

E. 45 cm

[Reveal] Spoiler: OA
OA in 24 hours, kudo for the right solution/explanation

The Pythagorean Theorem says: (leg)² + (other leg)² = (hypotenuse)²

We get: (20)² + (21)² = (hypotenuse)²
Evaluate: 400 + 441 = (hypotenuse)²
Evaluate: 841 = (hypotenuse)²
So, hypotenuse = √841 = 29

[Reveal] Spoiler:
C

Cheers,
Brent
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Re: If a right triangle has legs [#permalink]  14 Nov 2017, 09:04
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Here are three easy steps for answering any quant question on the GRE!

First, Survey the Question. Here you'll want to identify what skill is likely being tested. That will help you narrow down what kind of information you'll need to solve the question. Pay attention to mathy sounding words. Doing so here, the words "triangle" and "hypotenuse" and clues that we'll use either the Pythagorean Theorem or Pythagorean Triples.

Second, Develop a Plan. It's important that your plan takes place on your paper. Otherwise you'll waste time going 2 steps forward and 1 step backward (and even 2 steps backward sometimes!). We know that we want to use the Pythagorean Theorem, so let's write that down on our paper.

c^{2} = a^{2} + b^{2}

So the plan is shaping up here. We know that a=20 and b=21, so let's plan to plug in the numbers and finish this question!

Third, Solve the Question. Plugging in a and b into our equation we get:

c^{2} = 20^{2} + 21^{2}

c^{2} = 400 + 441

c^{2} = 841

So for c, we need the square root of 841. Now instead of trying to solve for it, let's estimate it instead. Think of a number close to 841 where you know it's square root. A good number here would be 900, as we know that the square root of 900 is 30. So the square root of 841 should be slightly less than 30. Looking at our answer choices, that eliminates D and E. A is way too small. B, 20.5, is less than one of our legs, and we know that the hypotenuse of a right triangle MUST be the longest side. So we're left with C as the only answer remaining. And we didn't even need to calculate the square root of 841!
Re: If a right triangle has legs   [#permalink] 14 Nov 2017, 09:04
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