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Basic Geometry : Right Triangles

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #1291 : Plane Geometry

Find the length of the hypotenuse.

Possible Answers:

$2\sqrt{111}$

$2\sqrt{106}$

Correct answer:

Explanation:

Use the Pythagorean Theorem to find the length of the hypotenuse, .

c^2=a^2+b^2

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

Substitute in the values for the legs, $a \text{ and }b$ , to find the length of the hypotenuse.

$c=\sqrt{(2\sqrt{2})^2+(\sqrt{73})^2}$

Simplify.

$c=\sqrt{81}$

Solve.

c=9

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Example Question #81 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse.

Possible Answers:

$12\sqrt2$

$9\sqrt3$

Correct answer:

Explanation:

Use the Pythagorean Theorem to find the length of the hypotenuse, .

c^2=a^2+b^2

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

Substitute in the values for the legs, $a \text{ and }b$ , to find the length of the hypotenuse.

$c=\sqrt{(4\sqrt{2})^2+7^2}$

Simplify.

$c=\sqrt{81}$

Solve.

c=9

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Example Question #82 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse.

Possible Answers:

$7\sqrt{70}$

$5\sqrt{142}$

$12\sqrt{3}$

Correct answer:

Explanation:

Use the Pythagorean Theorem to find the length of the hypotenuse, .

c^2=a^2+b^2

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

Substitute in the values for the legs, $a \text{ and }b$ , to find the length of the hypotenuse.

$c=\sqrt{(5\sqrt{2})^2+(\sqrt{71})^2}$

Simplify.

$c=\sqrt{121}$

Solve.

c=11

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Example Question #311 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$16\sqrt{2}$

$13\sqrt{5}$

Correct answer:

Explanation:

Use the Pythagorean Theorem to find the length of the hypotenuse, .

c^2=a^2+b^2

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

Substitute in the values for the legs, $a \text{ and }b$ , to find the length of the hypotenuse.

$c=\sqrt{(\sqrt{57})^2+8^2}$

Simplify.

$c=\sqrt{121}$

Solve.

c=11

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Example Question #312 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$6\sqrt{85}$

$12\sqrt{85}$

Correct answer:

Explanation:

Use the Pythagorean Theorem to find the length of the hypotenuse, .

c^2=a^2+b^2

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

Substitute in the values for the legs, $a \text{ and }b$ , to find the length of the hypotenuse.

$c=\sqrt{6^2+(\sqrt{85})^2}$

Simplify.

$c=\sqrt{121}$

Solve.

c=11

Report an Error

Example Question #313 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$12\sqrt{33}$

$2\sqrt{170}$

Correct answer:

Explanation:

Use the Pythagorean Theorem to find the length of the hypotenuse, .

c^2=a^2+b^2

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

Substitute in the values for the legs, $a \text{ and }b$ , to find the length of the hypotenuse.

$c=\sqrt{(2\sqrt{11})^2+10^2}$

Simplify.

$c=\sqrt{144}$

Solve.

c=12

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Example Question #86 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle has one side measuring 3in , and one side measuring 5in . The last and missing side is the hypotenuse. Find the length of the hypotenuse in inches.

Possible Answers:

5in

5.8in

10in

4.7in

6.2in

Correct answer:

5.8in

Explanation:

By using the Pythagorean Theorem a^2+b^2=c^2 , you find the correct answer of 5.8in .

This is done by plugging in 3=a , and 5=b , since was described as the hypotenuse. This gives us:

3^2 + 5^2 = c^2

9 + 25 = c^2

34 = c^2

$\sqrt{}34 = c$

5.8=c

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Example Question #121 : Right Triangles

Find the hypotenuse of a triangle whose side lengths are 10 and 3.

Possible Answers:

$\sqrt{109}$

$\sqrt{13}$

$\sqrt{103}$

$\sqrt{26}$

Correct answer:

$\sqrt{109}$

Explanation:

To solve, simply use the Pythagorean Theorem.

The hypotenuse is the c value in the equation and the two smaller leg lengths are a and b.

Let,

$\\a=10 \\b=3$

thus,

$\\c=\sqrt{a^2+b^2}\\c=\sqrt{10^2+3^2}\\c=\sqrt{100+9}\\c=\sqrt{109}$ .

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Example Question #122 : Right Triangles

Find the hypotenuse of a right triangle with width and length 3 and 5 respectively.

Possible Answers:

$\sqrt{15}$

$\sqrt{34}$

Correct answer:

$\sqrt{34}$

Explanation:

To find the diagonal of a rectangle recall that the diagonal will create a triangle where the width and length are legs of the triangle and the diagonal is the hypotenuse.

To solve, simple use the Pythagorean Theorem and solve for the hypotenuse, which will be the diagonal of the rectangle.

Thus,

$c=\sqrt{a^2+b^2}=\sqrt{3^2+5^2}=\sqrt{9+25}=\sqrt{34}$

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Example Question #89 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

The two shortest sides of a right triangle are each 10 cm . What is the length of the hypotenuse?

Possible Answers:

$2\sqrt{10}cm$

$10\sqrt{2}cm$

200cm

100cm

10cm

Correct answer:

$10\sqrt{2}cm$

Explanation:

The Pythagorean Theorem states that:

a^2+b^2=c^2

Because we know that and are both 10 cm , we can plug those in to find :

10^2+10^2=c^2

100+100=c^2

200=c^2

$c=\sqrt{200}=\sqrt{100}\times \sqrt{2} = 10\sqrt{2}$

Therefore, the triangle's hypotenuse is $10\sqrt{2}cm$ .

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Basic Geometry : Right Triangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #1291 : Plane Geometry

Example Question #81 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #82 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #311 : Triangles

Example Question #312 : Triangles

Example Question #313 : Triangles

Example Question #86 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #121 : Right Triangles

Example Question #122 : Right Triangles

Example Question #89 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

All Basic Geometry Resources

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