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Basic Geometry : Rectangles

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

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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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:

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

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Example Question #24 : 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:

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

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Example Question #25 : 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:

$100\pi$

$\sqrt{10}$

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:

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

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Example Question #26 : How To Find The Length Of The Diagonal Of A Rectangle

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:

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

$30\pi$

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:

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

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Example Question #27 : 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:

10000

100

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:

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

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Example Question #131 : Rectangles

If a rectangle is inscribed in a circle with a circumference of $16\pi$ , what is the length of the diagonal of the rectangle?

Possible Answers:

$32\pi$

196

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.

$\text{Diameter}=\frac{16\pi}{\pi}=16$

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

$\text{Diameter}=\text{Diagonal}=16$

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Example Question #131 : Rectangles

Find the length of the diagonal of a rectangle with side lengths 6 and 7.

Possible Answers:

$\sqrt{85}$

Correct answer:

$\sqrt{85}$

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,

$c=\sqrt{a^2+b^2}=\sqrt{36+49}=\sqrt{85}$

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Example Question #133 : Rectangles

A rectangle has a width of $5\;cm$ and a length that is $3\;cm$ shorter than twice the width. What is the length of the diagonal rounded to the nearest tenth?

Possible Answers:

$8.6\;cm$

$12.0\;cm$

$11.2\;cm$

$6.5\;cm$

$7.9\;cm$

Correct answer:

$8.6\;cm$

Explanation:

First we must find the length of the rectangle before we can solve for the diagonal. With a length $3\;cm$ shorter than twice the width, we can solve for length by drafting an algebraic equation:

$\\y=2x-3\;cm\\y=2(5\;cm)-3\;cm\\ y=10\;cm-3\;cm=7\;cm$

Now that we know the values for length and width, we can use the Pythagorean Theorem to solve for the diagonal:

$\\c^2=5^2\;+7^2\;=25+49=74\\c=\sqrt{74}\approx8.6\;cm$

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Basic Geometry : Rectangles

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

Example Question #25 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #26 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #27 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #131 : Rectangles

Example Question #131 : Rectangles

Example Question #133 : Rectangles

All Basic Geometry Resources

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