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Basic Geometry : Plane Geometry

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Example Questions

Example Question #162 : Plane Geometry

Righttriangle

Triangle ABC is a right triangle. If the length of side A = 8 inches and B = 11 inches, find the length of the hypoteneuse (to the nearest tenth).

Possible Answers:

185 inches

13.6 inches

184 inches

14.2 inches

13.7 inches

Correct answer:

13.6 inches

Explanation:

Using the Pythagrean Theorem, we know that $a^{2} + b^{2} = c^{2}$ .

This tells us:

$8^{2} + 11^{2} = C^{2}$

$64 + 121 = C^{2}$

$185 = C^{2}$

Taking the square root of both sides, we find that C = 13.6 inches

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Example Question #163 : Plane Geometry

Righttriangle

Given:

A = 6 feet

B = 9 feet

What is the length of the hypoteneuse of the triangle (to the nearest tenth)?

Possible Answers:

10.2 feet

10.8 feet

10.1 feet

10.6 feet

10.5 feet

Correct answer:

10.8 feet

Explanation:

Using the Pythagrean Theorem, we know that $a^{2} + b^{2} = c^{2}$ .

This tells us:

$6^{2} + 9^{2} = C^{2}$

$36 + 81 = C^{2}$

$117 = C^{2}$

Taking the square root of both sides, we find that C = 10.8

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Example Question #61 : Right Triangles

Righttriangle

Given:

A = 2 miles

B = 3 miles

What is the length of the hypoteneuse of triangle ABC, to the nearest tenth?

Possible Answers:

3.4 miles

3.6 miles

3.2 miles

3.7 miles

3.5 miles

Correct answer:

3.6 miles

Explanation:

Using the Pythagrean Theorem, we know that $a^{2} + b^{2} = c^{2}$ .

This tells us:

$2^{2} + 3^{2} = C^{2}$

$4 + 9 = C^{2}$

$13 = C^{2}$

Taking the square root of both sides, we find that C = 3.6

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Example Question #51 : Triangles

Given that two sides of a right triangle measure 2 feet and 3 feet, respectively, with a hypoteneuse of x, what is the perimeter of this right triangle (to the nearest tenth)?

Possible Answers:

18 feet

8.6 feet

9.4 feet

6.4 feet

3.6 feet

Correct answer:

8.6 feet

Explanation:

Using the Pythagrean Theorem, we know that $a^{2} + b^{2} = c^{2}$ .

This tells us:

$2^{2} + 3^{2} = C^{2}$

$4 + 9 = C^{2}$

$13 = C^{2}$

Taking the square root of both sides, we find that C = 3.6

To find the perimeter, we add the side lengths together, which gives us that the perimeter is: 3 + 2 + 3.6 = 8.6

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Example Question #43 : Right Triangles

$In\;\Delta GHJ, \;what\;is\;the\;length\;of\;\overline{GJ}?$

Possible Answers:

Correct answer:

Explanation:

$Use\;the\;Pythagorean\;Theorem:A^2+B^2=C^2,\;to\; find\;\overline{GJ}.$

5^2+12^2=C^2

25+144=C^2

169=C^2

$C=\sqrt{169}=13$

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Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Kathy and Jill are travelling from their home to the same destination. Kathy travels due east and then after travelling 6 miles turns and travels 8 miles due north. Jill travels directly from her home to the destination. How miles does Jill travel?

Possible Answers:

$\dpi{100} \small 12\ miles$

$\dpi{100} \small 14\ miles$

$\dpi{100} \small 10\ miles$

$\dpi{100} \small 8\ miles$

$\dpi{100} \small 16\ miles$

Correct answer:

$\dpi{100} \small 10\ miles$

Explanation:

Kathy's path traces the outline of a right triangle with legs of 6 and 8. By using the Pythagorean Theorem

$\dpi{100} \small 6^{2}+8^{2}=x^{2}$

$\dpi{100} \small 36+64=x^{2}$

$\dpi{100} \small x=10$ miles

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Example Question #51 : Triangles

$Which\; of \;the \;following \;is\; NOT\; true\; about \;the \;hypotenuse \;of \;a\; triangle?$

Possible Answers:

$It\;is\;always\;across\;from\;the\;largest\;angle\;in\;the\;triangle.$

$It\;is\;across\;from\;the\;right\;angle.$

$It\;is\;always\;greater\;than\;1.$

$It\;is\;the\;longest\;side.$

Correct answer:

$It\;is\;always\;greater\;than\;1.$

Explanation:

$The\;hypotenuse\;can\;be\;between\;0\;and\;1.$

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Example Question #1241 : Plane Geometry

What is the value of the hypotenuse of the right triangle ABC ?

Triangle_pythag

Possible Answers:

$5\sqrt{3}$

$5\sqrt{2}$

Correct answer:

Explanation:

There are two ways to solve this problem. The first is to recognize that the right triangle follows the pattern of a well-known Pythagorean triple: 5 - 12 - .

The second is to use the Pythagorean Theorem:

$A^{2}$ $B^{2}$ C^2 , where and are the lengths of the triangle sides and is the length of the hypotenuse.

Plugging in our values, we get:

5^2 12^2 C^2

C^2 169

C =

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Example Question #1242 : Plane Geometry

A right triangle has a base of 3 inches and a height of 5 inches. What is the length of the triangle's hypotenuse in inches?

Possible Answers:

6.45

5.83

2.8

Correct answer:

5.83

Explanation:

In a right triangle, the base and the height are the legs of the triangle. To find the hypotenuse, square both legs and add the results together. Then, find the square root of that sum.

$(3^{2})+(5^{2})=34$

$\sqrt{34}=5.83$

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Example Question #22 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

In order to get to work, Jeff leaves home and drives 4 miles due north, then 3 miles due east, followed by 6 miles due north and, finally, 7 miles due east. What is the straight line distance from Jeff’s work to his home?

Possible Answers:

2√5

6√2

10√2

Correct answer:

10√2

Explanation:

Jeff drives a total of 10 miles north and 10 miles east. Using the Pythagorean theorem (a²+b²=c²), the direct route from Jeff’s home to his work can be calculated. 10²+10²=c². 200=c². √200=c. √100√2=c. 10√2=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 #162 : Plane Geometry

Example Question #163 : Plane Geometry

Example Question #61 : Right Triangles

Example Question #51 : Triangles

Example Question #43 : Right Triangles

Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #51 : Triangles

Example Question #1241 : Plane Geometry

Example Question #1242 : Plane Geometry

Example Question #22 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

All Basic Geometry Resources

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