GMAT Math : Triangles

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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.)

Possible Answers:

$16\textup{ cm}$

$8.94\textup{ cm}$

$20\textup{ cm}$

$14.42 \textup{ cm}$

Correct answer:

$8.94\textup{ cm}$

Explanation:

We can calculate the length of the side by using the pythagorean theorem: c^2=a^2+b^2

where our values are c=12, a=8

we can then solve for :

12^2=8^2+x^2

x^2=12^2-8^2=80

x=8.94

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Example Question #2 : 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?

Possible Answers:

Correct answer:

Explanation:

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:

a^2+b^2=c^2

b^2=c^2-a^2=13^2-5^2=169-25

$b^2=144\rightarrow b=12$

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Example Question #3 : Calculating The Length Of The Side Of A Right Triangle

The hypotenuse of a $\textup{30-60-90}$ triangle has length $4^{t}$ . Which of the following is equal to the length of its shortest leg?

Possible Answers:

$4 ^{t-1}$

$4 ^{t-2}$

$4 ^{\frac{1}{2} t }$

$4 ^{\frac{1}{2} t-\frac{1}{2}}$

$4 ^{t-\frac{1}{2}}$

Correct answer:

$4 ^{t-\frac{1}{2}}$

Explanation:

The shortest leg of a $\textup{30-60-90}$ triangle is one half the length of its hypotenuse. In this triangle, it is

$\frac{1}{2} \cdot 4^{t} = \frac{4^{t}}{2} = \frac{4^{t}}{ \sqrt{4}} = \frac{4^{t}}{4^{\frac{1}{2}} } = 4 ^{t-\frac{1}{2}}$

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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:

a^2 + b^2 = c^2

5^2 + 12^2 = c^2

25 + 144 = c^2

169 = c^2

13 = c

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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:

$\dpi{100} \small 25$

$\dpi{100} \small 48$

$\dpi{100} \small 52$

$\dpi{100} \small 55$

$\dpi{100} \small 50$

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.

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

$hypotenuse = 50$

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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?

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:

a^2+b^2=c^2

8^2+15^2=c^2

c^2=64+225

$c^2=289\rightarrow c=\sqrt{289}=17$

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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 length and ?

Possible Answers:

$\sqrt{74}$

$\sqrt{15}$

$\sqrt{21}$

$\sqrt{75}$

$\sqrt{30}$

Correct answer:

$\sqrt{74}$

Explanation:

In order to find the value of the hypotenuse , we need to plug the values of the legs and into the Pythagorean Theorem: $a^{2}+b^{2}=c^{2}$

$5^{2}+7^{2}=c^{2}$

$25+49=c^{2}$

$74=c^{2}$

$\sqrt{74}=c$

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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 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 $A=\frac{1}{2}ab$ :

2A=ab

$\frac{2A}{b}=a$

Plugging in and :

$\frac{2(30)}{12}=a$

$\frac{60}{12}=a$

5=a

Now we need to plug the values of the legs and into the Pythagorean Theorem: $a^{2}+b^{2}=c^{2}$

$5^{2}+12^{2}=c^{2}$

$25+144=c^{2}$

$169=c^{2}$

13=c

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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 lengths 7cm and 9cm ?

Possible Answers:

15cm

$\sqrt{65}cm$

$\sqrt{70}cm$

12cm

$\sqrt{130}cm$

Correct answer:

$\sqrt{130}cm$

Explanation:

In order to find the value of the hypotenuse , we need to plug the values of the legs and into the Pythagorean Theorem: $a^{2}+b^{2}=c^{2}$

$(7cm)^{2}+(9cm)^{2}=c^{2}$

$49cm+81cm=c^{2}$

$130cm=c^{2}$

$\sqrt{130}cm=c$

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Example Question #7 : Calculating The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Each leg of a $\textup{45-45-90}$ triangle has length $2 ^{K}$ . Give the length of its hypotenuse.

Possible Answers:

$2 ^{ \frac{1}{2}K }$

$2 ^{K +1}$

$2 ^{K + \frac{1}{2}}$

$2 ^{ 2K }$

$2 ^{K - \frac{1}{2}}$

Correct answer:

$2 ^{K + \frac{1}{2}}$

Explanation:

The hypotenuse of a $\textup{45-45-90}$ triangle has length $\sqrt{2} = 2^{\frac{1}{2}}$ times that of a leg, which here is

$2 ^{K} \cdot 2^{\frac{1}{2}} = 2 ^{K+ \frac{1}{2}}$ .

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GMAT Math : Triangles

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Calculating The Length Of The Side Of A Right Triangle

Example Question #2 : Calculating The Length Of The Side Of A Right Triangle

Example Question #3 : Calculating The Length Of The Side Of A Right Triangle

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

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

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

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

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

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

Example Question #7 : Calculating The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

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