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Basic Geometry : How to find the length of the diagonal of a rectangle

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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 #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 $3\pi$ , 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 #22 : 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 $2\pi$ , 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 #22 : 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:

$\sqrt2$

$\frac{\sqrt2}{2}$

$2\sqrt2$

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:

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

Report an Error

Example Question #23 : 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:

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

Report an Error

Example Question #23 : How To Find The Length Of The Diagonal Of A Rectangle

If a rectangle is inscribed in a circle with a circumference of $\sqrt3\pi$ , what is the length of the diagonal of the rectangle?

Possible Answers:

$\sqrt3$

Correct answer:

$\sqrt3$

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.

$\text{Diameter}=\frac{\sqrt3\pi}{\pi}=\sqrt3$

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

$\text{Diameter}=\text{Diagonal}=\sqrt3$

Report an Error

Example Question #23 : How To Find The Length Of The Diagonal Of A Rectangle

If a rectangle is inscribed in a circle with a circumference of $8\pi$ , what is the length of the diagonal of the rectangle?

Possible Answers:

$2\pi$

$2\sqrt2$

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.

$\text{Diameter}=\frac{8\pi}{\pi}=8$

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

$\text{Diameter}=\text{Diagonal}=8$

Report an Error

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

If a rectangle is inscribed in a circle with a circumference of $10\pi$ , what is the length of the diagonal of the rectangle?

Possible Answers:

$\sqrt{10}$

$100\pi$

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.

$\text{Diameter}=\frac{10\pi}{\pi}=10$

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

$\text{Diameter}=\text{Diagonal}=10$

Report an Error

Example Question #131 : Rectangles

If a rectangle is inscribed in a circle with a circumference of $15\pi$ , what is the length of the diagonal of the rectangle?

Possible Answers:

$30\pi$

$\frac{15\pi}{2}$

225

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.

$\text{Diameter}=\frac{15\pi}{\pi}=15$

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

$\text{Diameter}=\text{Diagonal}=15$

Report an Error

Example Question #30 : How To Find The Length Of The Diagonal Of A Rectangle

If a rectangle is inscribed in a circle with a circumference of $100\pi$ , what is the length of the diagonal of the rectangle?

Possible Answers:

100

10000

Correct answer:

100

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.

$\text{Diameter}=\frac{100\pi}{\pi}=100$

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

$\text{Diameter}=\text{Diagonal}=100$

Report an Error

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Basic Geometry : How to find the length of the diagonal of a rectangle

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #21 : 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 #22 : 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

Example Question #23 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #23 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #23 : 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 #131 : Rectangles

Example Question #30 : How To Find The Length Of The Diagonal Of A Rectangle

All Basic Geometry Resources

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