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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 #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

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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 #81 : 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:

6.2in

4.7in

5.8in

5in

10in

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 #321 : Triangles

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

Possible Answers:

$\sqrt{26}$

$\sqrt{109}$

$\sqrt{13}$

$\sqrt{103}$

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 #322 : 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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Example Question #90 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse using Pythagorean Theorem.

The triangle has two other sides with lengths 3 and 4 inches.

Possible Answers:

$25\ inches$

$50\ inches$

$5\ inches$

$12\ inches$

$10\ inches$

Correct answer:

$5\ inches$

Explanation:

The formula for Pythagorean Theorem is, A^2 + B^2 = C^2

C is the hypotenuse and A and B are the other two sides. To begin Pythagorean Theorem the order of A and B does not matter.

If A is 3 and B is 4 then,

3^2 + 4^2 = C^2

9 + 16 = C^2

25 = C^2

You must find C and not c squared. Therefore to get rid of the squared you must do the opposite of squaring something, which is the square root of something.

$\sqrt{25} = \sqrt{C^2}$

5 = C

5 inches

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Example Question #321 : Triangles

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

$3\sqrt{21}$

$2\sqrt{29}$

$4\sqrt5$

$\sqrt{29}$

Correct answer:

$2\sqrt{29}$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{10^2 + 4^2}=\sqrt{116}$

Simply:

$\sqrt{4}\cdot\sqrt{29}$

$2\sqrt{29}$

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Example Question #74 : Right Triangles

Justin travels $15\textup{ feet}$ to the east and $20\textup{ feet}$ to the north. How far away from his starting point is he now?

Possible Answers:

$45\textup{ ft}$

$35\textup{ ft}$

$25\textup{ ft}$

$22\textup{ ft}$

$30\textup{ ft}$

Correct answer:

$25\textup{ ft}$

Explanation:

This is solving for the hypotenuse of a triangle. Using the Pythagorean Theorem, which says that a^2+b^2=c^2

15^2 + 20^2 = c^2

225+400=c^2

625=c^2

25=c

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #311 : Triangles

Example Question #312 : Triangles

Example Question #313 : Triangles

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

Example Question #321 : Triangles

Example Question #322 : Triangles

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

Example Question #90 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #321 : Triangles

Example Question #74 : Right Triangles

All Basic Geometry Resources

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