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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #301 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$12\sqrt6$

$8\sqrt{55}$

Correct answer:

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.

$c^2=(4\sqrt{11})^2+(2\sqrt{5})^2$

Simplify.

c^2=176+20

Solve.

c^2=196

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

$\sqrt{c^2}=\sqrt{196}$

Simplify.

c=14

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Example Question #74 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse.

Possible Answers:

$4\sqrt{6}$

$2\sqrt{231}$

$12\sqrt{11}$

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.

$c=\sqrt{(\sqrt{22})^2+(\sqrt{42})^2}$

Simplify.

$c=\sqrt{64}$

Solve.

c=8

Report an Error

Example Question #75 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse.

Possible Answers:

$6\sqrt{23}$

$6\sqrt{7}$

$8\sqrt{14}$

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.

$c=\sqrt{(3\sqrt{2})^2+(\sqrt{46})^2}$

Simplify.

$c=\sqrt{64}$

Solve.

c=8

Report an Error

Example Question #311 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$2\sqrt{113}$

$8\sqrt2$

$12\sqrt5$

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.

$c=\sqrt{(\sqrt{30})^2+(\sqrt{34})^2}$

Simplify.

$c=\sqrt{64}$

Solve.

c=8

Report an Error

Example Question #312 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$3\sqrt{33}$

$2\sqrt{119}$

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.

$c=\sqrt{(\sqrt{21})^2+(\sqrt{43})^2}$

Simplify.

$c=\sqrt{64}$

Solve.

c=8

Report an Error

Example Question #313 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$3\sqrt{95}$

$2\sqrt{303}$

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.

$c=\sqrt{(\sqrt{21})^2+(2\sqrt{15})^2}$

Simplify.

$c=\sqrt{81}$

Solve.

c=9

Report an Error

Example Question #314 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$\sqrt{770}$

$11\sqrt{2}$

$12\sqrt{7}$

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.

$c=\sqrt{(\sqrt{11})^2+(\sqrt{70})^2}$

Simplify.

$c=\sqrt{81}$

Solve.

c=9

Report an Error

Example Question #121 : Right Triangles

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

Report an Error

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

Report an Error

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

Report an Error

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #301 : Triangles

Example Question #74 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #75 : 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 #314 : Triangles

Example Question #121 : Right Triangles

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

All Basic Geometry Resources

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