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Basic Geometry : How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

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Example Question #101 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Prblem 6 basic geometry

Find the length of the hypotenuse in triangle ABC

Possible Answers:

$15\ inches$

$91\ inches$

$\sqrt{400}inches$

$\sqrt{256}inches$

$\sqrt{365}inches$

Correct answer:

$\sqrt{365}inches$

Explanation:

To find the length of the hypotenuse, use the Pythagorean Theorem.

a^2+b^2=c^2

a=14 inches

b=13 inches

c=???

14^2+13^2=c^2

196 + 169 = 365

365=c^2

Now take the square root of both sides.

$\sqrt{365}=c$

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Example Question #102 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Three sides of a right triangle are A,B, and C. Side C is the hypotenuse.

A=3 . B=4 . Find .

Possible Answers:

C=7

C=25

C=5

C=4

Correct answer:

C=5

Explanation:

To solve for the value of c, you would use the Pythagorean theorem, which states

A^2+B^2=C^2 .

Plugging in the values we have, we get

3^2+4^2=C^2 .

To solve for c, we take the square root of both sides.

$\sqrt{3^2+4^2}=\sqrt {C^2}$ .

$\sqrt{25}=5=C$ .

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Example Question #141 : Right Triangles

What is the hypotenuse, , of a triangle whose other sides are A=9 and B=40 .

Possible Answers:

C=42

C=40

C=41

C=20

Correct answer:

C=41

Explanation:

To find the length of the hypotenuse, we must use the Pythagorean Theorem,

A^2+B^2=C^2 .

Using the values given,

$9^2+41^2=C^2\rightarrowC=\sqrt{81+1681}=42$ .

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Example Question #101 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse of a triangle with legs 3 and 7.

Possible Answers:

$\sqrt{52}$

$\sqrt{58}$

$\sqrt{40}$

Correct answer:

$\sqrt{58}$

Explanation:

Use Pythagorean Theorem: 3^2 + 7^2 = c^2

9 + 49 = c^2

58 = c^2

$\sqrt{58 } = c$

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Example Question #1322 : Plane Geometry

Shape area right triangle

In the right triangle shown here, a=8 and b=15 . What is the length of the remaining side?

Possible Answers:

Correct answer:

Explanation:

By the Pythagorean Theorem, the relationship between a right triangle's height , its base , and its hypotenuse is given by

a^2+b^2=c^2 .

Here, a=8 and b=15 . The length of the remaining side can be calculated as follows:

a^2+b^2=c^2

8^2+15^2=c^2

64+225=c^2

289=c^2

$\Rightarrow c= \sqrt{289}=17$ .

Hence, the length of this right triangle's hypotenuse is units.

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Example Question #1323 : Basic Geometry

If one leg of a right triangle is 6in and the other leg is 8in, what is the measure of the hypotenuse?

Possible Answers:

$9\text{ in}$

$12\text{ in}$

$10\text{ in}$

$11\text{ in}$

$14\text{ in}$

Correct answer:

$10\text{ in}$

Explanation:

First we need to know Pythagorean Theorem states that what when we take the square of one leg and add it to the square of the other leg, we get the hypotenuse squared or $a^{2}+b^{2}=c^{2}$ where a and b represent the short legs and c represents the hypotenuse (long side of the triangle opposite the right angle).

Since the short legs of our triangles are 6 and 8 we can set up our equation as follows:

$6^{2}+8^{2}=c^{2}$

Now we solve

36 + 64 =100

Since $c^{2}=100$ we take the square root of both sides and we get c=10 .

So the hypotenuse measures 10 inches.

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Example Question #81 : Triangles

Susie walks north from her house to a park that is 30 meters away. Once she arrives at the park, she turns and walks west for 80 meters to a bench to feed some pigeons. She then walks north for another 30 meters to a concession stand. If Susie returns home in a straight line from the concession stand, how far will she walk from the concession stand to her house, in meters?

Possible Answers:

100

200

Correct answer:

100

Explanation:

Susie walks 30 meters north, then 80 meters west, then 30 meters north again. Thus, she walks 60 meters north and 80 meters west. These two directions are 90 degrees away from one another.

At this point, construct a right triangle with one leg that measures 60 meters and a second leg that is 80 meters.

You can save time by using the 3:4:5 common triangle. 60 and 80 are $3\cdot 20$ and $4\cdot 20$ , respectively, making the hypotenuse equal to $5\cdot 20=100$ .

We can solve for the length of the missing hypotenuse by applying the Pythagorean theorem:

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

Substitute the following known values into the formula and solve for the missing hypotenuse: side .

$a= 60,\ b= 80,\ c= ?$

$(60)^{2}+(80)^{2}=c^{2}$

$3600+6400=c^{2}$

$10,000=c^{2}$

c=100

Susie will walk 100 meters to reach her house.

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Example Question #82 : Triangles

The lengths of the sides of a triangle are consecutive odd numbers and the triangle's perimeter is 57 centimeters. What is the length, in centimeters, of its longest side?

Possible Answers:

Correct answer:

Explanation:

First, define the sides of the triangle. Because the side lengths are consecutive odd numbers, if we define the shortest side will be as , the next side will be defined as x+2 , and the longest side will be defined as x+4 . We can then find the perimeter of a triangle using the following formula:

$\text{Perimeter}=\text{side}+\text{side}+\text{side}$

Substitute in the known values and variables.

$\text{Perimeter}=x+(x+2)+(x+4)$

57=3x+6

Subtract 6 from both sides of the equation.

57-6=3x+6-6

51=3x

Divide both sides of the equation by 3.

$\frac{51}{3}=\frac{3x}{3}$

Solve.

x=17

This is not the answer; we need to find the length of the longest side, or x+4 .

$\text{Longest side}=x+4$

Substitute in the calculated value for and solve.

$\text{Longest side}=17+4$

$\text{Longest side}=21$

The longest side of the triangle is 21 centimeters long.

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Example Question #1324 : Basic Geometry

Each of the following answer choices lists the side lengths of a different triangle. Which of these triangles does not have a right angle?

Possible Answers:

9, 12, 15

$2, 2, 2\sqrt{2}$

6,7,12

5, 12, 13

Correct answer:

6,7,12

Explanation:

6, 7, 12 cannot be the side lengths of a right triangle. 6^2+ 7^2 does not equal 12^2 . Also, special right triangle 3-4-5, 5-12-13, and 45-45-90 rules can eliminate all the other choices.

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Example Question #101 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse.

Possible Answers:

$5\sqrt{10}$

$2\sqrt{10}$

$4\sqrt{10}$

Correct answer:

$2\sqrt{10}$

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(2\sqrt{5})^2+(2\sqrt{5})^2$

Simplify.

c^2=20+20

Solve.

c^2=40

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=\sqrt{40}$

Simplify.

$c=2\sqrt{10}$

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Basic Geometry : How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #101 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #102 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #141 : Right Triangles

Example Question #101 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #1322 : Plane Geometry

Example Question #1323 : Basic Geometry

Example Question #81 : Triangles

Example Question #82 : Triangles

Example Question #1324 : Basic Geometry

Example Question #101 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

All Basic Geometry Resources

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