All GMAT Math Resources
Example Questions
Example Question #1 :Calculating The Length Of The Side Of A Right Triangle
Calculate the length of the side of the following right triangle.
(Not drawn to scale.)
We can calculate the length of the side by using the pythagorean theorem:
where our values are
we can then solve for:
Example Question #1 :Calculating The Length Of The Side Of A Right Triangle
A right triangle has a hypotenuse of 13 and a height of 5. What is the length of the third side of the triangle?
In order to find the length of the third side, we need to use the Pythagorean theorem. The hypotenuse, c, is 13, and the height, a, is 5, so we can simply plug in these values and solve for b, the length of the base of the right triangle:
Example Question #3 :Calculating The Length Of The Side Of A Right Triangle
The hypotenuse of atriangle has length. Which of the following is equal to the length of its shortest leg?
The shortest leg of atriangle is one half the length of its hypotenuse. In this triangle, it is
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 areandunits long?
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?
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.
Example Question #3 :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?
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 #1 :Calculating The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem
What is the hypotenuse of a right triangle with legs of lengthand?
In order to find the value of the hypotenuse, we need to plug the values of the legsandinto 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 an area ofand a leg length of?
In order to find the value of the hypotenusegiven areaand leg length, we first need to calculate the length of the other leg length. Given the area equation:
Plugging inand:
Now we need to plug the values of the legsandinto the Pythagorean Theorem:
Example Question #6 :Calculating The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem
What is the hypotenuse of a right triangle with legs of lengthsand?
In order to find the value of the hypotenuse, we need to plug the values of the legsandinto the Pythagorean Theorem:
Example Question #7 :Calculating The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem
Each leg of atriangle has length. Give the length of its hypotenuse.
The hypotenuse of atriangle has lengthtimes that of a leg, which here is
.