GMAT Math : Calculating the length of the hypotenuse of a right triangle : Pythagorean Theorem

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #1 : Calculating The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

What is the length of a right triangle hypotenuse if the the other two sides are and units long?

Possible Answers:

Correct answer:

Explanation:

To find a length of a side in a right triangle, we can use the Pythagorean theorem:

Example Question #1 : Calculating The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

What is the hypotenuse of a right triangle with sides 14 and 48?

Possible Answers:

\dpi{100} \small 55

\dpi{100} \small 52

\dpi{100} \small 48

\dpi{100} \small 25

\dpi{100} \small 50

Correct answer:

\dpi{100} \small 50

Explanation:

For starters, we know that the hypotenuse is the longest side of a triangle, so we can immediately cross off 25 as an answer choice because it is smaller than one of the legs, 48. To find the hypotenuse, we can use  the Pythagorean Theorem.

hypotenuse^{^{2}} = 14^{2} + 48^{2} = 2500

hypotenuse = 50

 

Example Question #2 : Calculating The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle has a height of 8 and a base of 15. What is the length of its hypotenuse? 

Possible Answers:

Correct answer:

Explanation:

We are given the length of the height and the base, so we can use the Pythagorean theorem to calculate the length of the hypotenuse:

Example Question #3 : Calculating The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

What is the hypotenuse of a right triangle with legs of length  and ?

Possible Answers:

Correct answer:

Explanation:

In order to find the value of the hypotenuse , we need to plug the values of the legs  and  into the Pythagorean Theorem: 

 

Example Question #4 : Calculating The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

What is the hypotenuse of a right triangle with an area of  and a leg length of ?

Possible Answers:

Correct answer:

Explanation:

In order to find the value of the hypotenuse  given area  and leg length , we first need to calculate the length of the other leg length . Given the area equation :

Plugging in  and :

Now we need to plug the values of the legs  and  into the Pythagorean Theorem: 

Example Question #5 : Calculating The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

What is the hypotenuse of a right triangle with legs of lengths  and ?

Possible Answers:

Correct answer:

Explanation:

In order to find the value of the hypotenuse , we need to plug the values of the legs  and  into the Pythagorean Theorem: 

Example Question #6 : Calculating The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Each leg of a  triangle has length . Give the length of its hypotenuse.

Possible Answers:

Correct answer:

Explanation:

The hypotenuse of a  triangle has length  times that of a leg, which here is

.

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