GMAT Math : Problem-Solving Questions

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #12 : Right Triangles

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 #501 : Problem Solving Questions

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

Possible Answers:

\dpi{100} \small 52

\dpi{100} \small 55

\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 #14 : Right Triangles

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 #12 : Right Triangles

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 #16 : Triangles

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 #4 : 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 #3 : 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

.

Example Question #262 : Geometry

What is the perimeter of a  traingle?

Possible Answers:

Correct answer:

Explanation:

A triangle is a right triangle. To find the perimeter, we must add up all the sides of the triangle.

Example Question #21 : Right Triangles

A right triangle has a hypotenuse of length 13 yards and a leg of length 5 yards. Give the perimeter of this triangle in inches.

Possible Answers:

Correct answer:

Explanation:

We can use the Pythagorean Theorem to calculate the length of the second leg  in yards of the triangle by setting  in this formula:

The perimeter of the triangle is yards is 

 yards. Multiply this by 36 to covert to inches:

 inches.

 

Example Question #3 : Calculating The Perimeter Of A Right Triangle

A right triangle has legs of length  feet and and   feet. Give the perimeter of this triangle in yards.

Possible Answers:

Correct answer:

Explanation:

We can use the Pythagorean Theorem to calculate the hypotenuse  of the triangle by setting  in this formula:

The perimeter is  feet. 

Divide by 3 to convert to yards:

 yards

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