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Basic Geometry : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

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All Basic Geometry Resources

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

Example Questions

Example Question #531 : Plane Geometry

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

Possible Answers:

$\sqrt{178}$

$\sqrt{221}$

$\sqrt{110}$

$\sqrt{222}$

Correct answer:

$\sqrt{221}$

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,

$\text{Diagonal}=\sqrt{10^2+11^2}=\sqrt{221}$

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Example Question #11 : How To Find The Length Of The Diagonal Of A Rectangle

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

Possible Answers:

$2\sqrt{85}$

$2\sqrt{83}$

$2\sqrt{87}$

Correct answer:

$2\sqrt{85}$

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,

$\text{Diagonal}=\sqrt{14^2+12^2}=\sqrt{340}=2\sqrt{85}$

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Example Question #15 : 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:

$12\sqrt2$

$6\sqrt{11}$

$4\sqrt{17}$

$18\sqrt3$

Correct answer:

$4\sqrt{17}$

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,

$\text{Diagonal}=\sqrt{4^2+16^2}=\sqrt{272}=4\sqrt{17}$

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Example Question #121 : Quadrilaterals

Find the length of the diagonal of a rectangle whose length is 5 and width is 3.

Possible Answers:

$\sqrt{15}$

$\sqrt{34}$

Correct answer:

$\sqrt{34}$

Explanation:

To solve, simply use the pythagorean theorem. Thus,

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

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

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Example Question #17 : How To Find The Length Of The Diagonal Of A Rectangle

A rectangle is inscribed in a circle. If the circumference of the circle is $5\pi$ , what is the length of the diagonal of the rectangle?

Possible Answers:

Correct answer:

Explanation:

You should notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall how to find the circumference of a circle.

$\text{Circumference}=\text{diameter}\times\pi$

Since we are given the circumference and need the diameter, rerwite the equation to solve for the diameter.

$\text{Diameter}=\frac{\text{Circumference}}{\pi}$

Plug in the given circumference to find the diameter.

$\text{Diameter}=\frac{5\pi}{\pi}=5$

Now, recall the relationship between the diameter of the circle and the diagonal of the rectangle:

$\text{Diameter}=\text{Diagonal}=5$

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Example Question #21 : How To Find The Length Of The Diagonal Of A Rectangle

A rectangle is inscribed in a circle. If the circumference of the circle is $4\pi$ , what is the length of the diagonal of the rectangle?

Possible Answers:

Correct answer:

Explanation:

You should notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall how to find the circumference of a circle.

$\text{Circumference}=\text{diameter}\times\pi$

Since we are given the circumference and need the diameter, rerwite the equation to solve for the diameter.

$\text{Diameter}=\frac{\text{Circumference}}{\pi}$

Plug in the given circumference to find the diameter.

$\text{Diameter}=\frac{4\pi}{\pi}=4$

Now, recall the relationship between the diameter of the circle and the diagonal of the rectangle:

$\text{Diameter}=\text{Diagonal}=4$

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Example Question #122 : Quadrilaterals

A rectangle is inscribed in a circle. If the circumference of the circle is $3\pi$ , what is the length of the diagonal of the rectangle?

Possible Answers:

$\frac{3}{2}$

Correct answer:

Explanation:

You should notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall how to find the circumference of a circle.

$\text{Circumference}=\text{diameter}\times\pi$

Since we are given the circumference and need the diameter, rerwite the equation to solve for the diameter.

$\text{Diameter}=\frac{\text{Circumference}}{\pi}$

Plug in the given circumference to find the diameter.

$\text{Diameter}=\frac{3\pi}{\pi}=3$

Now, recall the relationship between the diameter of the circle and the diagonal of the rectangle:

$\text{Diameter}=\text{Diagonal}=3$

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Example Question #130 : Quadrilaterals

A rectangle is inscribed in a circle. If the circumference of the circle is $2\pi$ , what is the length of the diagonal of the rectangle?

Possible Answers:

The diagonal of the rectangle cannot be determined.

Correct answer:

Explanation:

You should notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall how to find the circumference of a circle.

$\text{Circumference}=\text{diameter}\times\pi$

Since we are given the circumference and need the diameter, rerwite the equation to solve for the diameter.

$\text{Diameter}=\frac{\text{Circumference}}{\pi}$

Plug in the given circumference to find the diameter.

$\text{Diameter}=\frac{2\pi}{\pi}=2$

Now, recall the relationship between the diameter of the circle and the diagonal of the rectangle:

$\text{Diameter}=\text{Diagonal}=2$

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Example Question #21 : How To Find The Length Of The Diagonal Of A Rectangle

A rectangle is inscribed in a circle. If the circumference of the circle is $\sqrt2\pi$ , what is the length of the diagonal of the rectangle?

Possible Answers:

$\sqrt2$

$2\sqrt2$

$\frac{\sqrt2}{2}$

Correct answer:

$\sqrt2$

Explanation:

You should notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall how to find the circumference of a circle.

$\text{Circumference}=\text{diameter}\times\pi$

Since we are given the circumference and need the diameter, rerwite the equation to solve for the diameter.

$\text{Diameter}=\frac{\text{Circumference}}{\pi}$

Plug in the given circumference to find the diameter.

$\text{Diameter}=\frac{\sqrt2\pi}{\pi}=\sqrt2$

Now, recall the relationship between the diameter of the circle and the diagonal of the rectangle:

$\text{Diameter}=\text{Diagonal}=\sqrt2$

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Example Question #22 : How To Find The Length Of The Diagonal Of A Rectangle

If a rectangle is inscribed in a circle with a circumference of $12\pi$ , what is the length of the diagonal of the rectangle?

Possible Answers:

144

Correct answer:

Explanation:

You should notice that the diagonal of the rectangle is the same as the diameter of the circle.

Now, recall how to find the circumference of a circle.

$\text{Circumference}=\text{diameter}\times\pi$

Since we are given the circumference and need the diameter, rerwite the equation to solve for the diameter.

$\text{Diameter}=\frac{\text{Circumference}}{\pi}$

Plug in the given circumference to find the diameter.

$\text{Diameter}=\frac{12\pi}{\pi}=12$

Now, recall the relationship between the diameter of the circle and the diagonal of the rectangle:

$\text{Diameter}=\text{Diagonal}=12$

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All Basic Geometry Resources

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Basic Geometry : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #531 : Plane Geometry

Example Question #11 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #15 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #121 : Quadrilaterals

Example Question #17 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #21 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #122 : Quadrilaterals

Example Question #130 : Quadrilaterals

Example Question #21 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #22 : How To Find The Length Of The Diagonal Of A Rectangle

All Basic Geometry Resources

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