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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 #4 : How To Find The Length Of The Diagonal Of A Rectangle

The sides of rectangle ABCD are 4 in and 13 in.

How long is the diagonal of rectangle ABCD?

Possible Answers:

$\sqrt{125}$

$\sqrt{185}$

185

Correct answer:

$\sqrt{185}$

Explanation:

A diagonal of a rectangle cuts the rectangle into 2 right triangles with sides equal to the sides of the rectangle and with a hypotenuse that is the diagonal. All you need to do is use the pythagorean theorem:

a^2+b^2=c^2 where a and b are the sides of the rectangle and c is the length of the diagonal.

$\sqrt{4^2+16^2}=\sqrt{185}=c$

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Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Find the length of the diagonal of a rectangle that has a length of and a width of .

Possible Answers:

Correct answer:

Explanation:

The diagonal of a rectangle is also the hypotenuse of a right triangle that has the length and the width of the rectangle as its legs.

We can then use the Pythgorean Theorem to find the diagonal.

$\text{Diagonal}=\sqrt{\text{length}^2+\text{width}^2}$

For the given rectangle,

$\text{Diagonal}=\sqrt{9^2+12^2}=\sqrt{225}=15$

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Example Question #5 : How To Find The Length Of The Diagonal Of A Rectangle

Find the length of the diagonal of a rectangle that has a length of and a width of .

Possible Answers:

Correct answer:

Explanation:

The diagonal of a rectangle is also the hypotenuse of a right triangle that has the length and the width of the rectangle as its legs.

We can then use the Pythgorean Theorem to find the diagonal.

$\text{Diagonal}=\sqrt{\text{length}^2+\text{width}^2}$

For the given rectangle,

$\text{Diagonal}=\sqrt{10^2+24^2}=\sqrt{676}=26$

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Example Question #3 : How To Find The Length Of The Diagonal Of A Rectangle

Find the length of the diagonal of a rectangle that has a length of and a width of .

Possible Answers:

Correct answer:

Explanation:

The diagonal of a rectangle is also the hypotenuse of a right triangle that has the length and the width of the rectangle as its legs.

We can then use the Pythgorean Theorem to find the diagonal.

$\text{Diagonal}=\sqrt{\text{length}^2+\text{width}^2}$

For the given rectangle,

$\text{Diagonal}=\sqrt{6^2+8^2}=\sqrt{100}=10$

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Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Find the length of the diagonal of a rectangle that has a length of and a width of .

Possible Answers:

$12\sqrt{35}$

$3\sqrt{34}$

$6\sqrt{2}$

$4\sqrt3$

Correct answer:

$3\sqrt{34}$

Explanation:

The diagonal of a rectangle is also the hypotenuse of a right triangle that has the length and the width of the rectangle as its legs.

We can then use the Pythgorean Theorem to find the diagonal.

$\text{Diagonal}=\sqrt{\text{length}^2+\text{width}^2}$

For the given rectangle,

$\text{Diagonal}=\sqrt{9^2+15^2}=\sqrt{306}=3\sqrt{34}$

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Example Question #111 : Rectangles

Find the length of the diagonal of a rectangle that has a length of and a width of .

Possible Answers:

$16\sqrt{3}$

$15\sqrt{29}$

Correct answer:

Explanation:

The diagonal of a rectangle is also the hypotenuse of a right triangle that has the length and the width of the rectangle as its legs.

We can then use the Pythgorean Theorem to find the diagonal.

$\text{Diagonal}=\sqrt{\text{length}^2+\text{width}^2}$

For the given rectangle,

$\text{Diagonal}=\sqrt{13^2+84^2}=\sqrt{7225}=85$

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Example Question #521 : Plane Geometry

Find the length of the diagonal of a rectangle that has a length of and a width of .

Possible Answers:

$6\sqrt3$

$\sqrt{13}$

$2\sqrt{5}$

$\sqrt{7}$

Correct answer:

$\sqrt{13}$

Explanation:

The diagonal of a rectangle is also the hypotenuse of a right triangle that has the length and the width of the rectangle as its legs.

We can then use the Pythgorean Theorem to find the diagonal.

$\text{Diagonal}=\sqrt{\text{length}^2+\text{width}^2}$

For the given rectangle,

$\text{Diagonal}=\sqrt{2^2+3^2}=\sqrt{13}$

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Example Question #112 : Quadrilaterals

Find the length of the diagonal of a rectangle that has a length of and a width of .

Possible Answers:

$2\sqrt{15}$

$2\sqrt{13}$

$2\sqrt{19}$

$2\sqrt{17}$

Correct answer:

$2\sqrt{17}$

Explanation:

The diagonal of a rectangle is also the hypotenuse of a right triangle that has the length and the width of the rectangle as its legs.

We can then use the Pythgorean Theorem to find the diagonal.

$\text{Diagonal}=\sqrt{\text{length}^2+\text{width}^2}$

For the given rectangle,

$\text{Diagonal}=\sqrt{8^2+2^2}=\sqrt{68}=2\sqrt{17}$

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Example Question #521 : Basic Geometry

Find the length of the diagonal of a rectangle that has a length of and a width of .

Possible Answers:

$\sqrt{29}$

$\sqrt{31}$

$3\sqrt3$

Correct answer:

$\sqrt{29}$

Explanation:

The diagonal of a rectangle is also the hypotenuse of a right triangle that has the length and the width of the rectangle as its legs.

We can then use the Pythgorean Theorem to find the diagonal.

$\text{Diagonal}=\sqrt{\text{length}^2+\text{width}^2}$

For the given rectangle,

$\text{Diagonal}=\sqrt{5^2+2^2}=\sqrt{29}$

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Example Question #12 : How To Find The Length Of The Diagonal Of A Rectangle

Find the length of the diagonal of a rectangle that has a length of and a width of .

Possible Answers:

$2\sqrt{29}$

$6\sqrt3$

$2\sqrt{31}$

Correct answer:

$2\sqrt{29}$

Explanation:

The diagonal of a rectangle is also the hypotenuse of a right triangle that has the length and the width of the rectangle as its legs.

We can then use the Pythgorean Theorem to find the diagonal.

$\text{Diagonal}=\sqrt{\text{length}^2+\text{width}^2}$

For the given rectangle,

$\text{Diagonal}=\sqrt{4^2+10^2}=\sqrt{116}=2\sqrt{29}$

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All Basic Geometry Resources

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #4 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #5 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #3 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #111 : Rectangles

Example Question #521 : Plane Geometry

Example Question #112 : Quadrilaterals

Example Question #521 : Basic Geometry

Example Question #12 : How To Find The Length Of The Diagonal Of A Rectangle

All Basic Geometry Resources

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