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Basic Geometry : Basic 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 #41 : How To Find The Perimeter Of A Square

Find the perimeter of a square inscribed in a circle that has a diameter of $19\sqrt2$ .

Possible Answers:

104

$76\sqrt2$

Correct answer:

Explanation:

Notice that the diameter of the circle is also the diagonal of the square. The diagonal of the square is also the hypotenuse of a right isosceles triangle that has the sides of the square as its legs.

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

$\text{Diagonal}^2=\text{side}^2+\text{side}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{19\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=19$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(19)$

Solve.

$\text{Perimeter}=76$

Report an Error

Example Question #484 : Quadrilaterals

Find the perimeter of a square inscribed in a circle that has a diameter of .

Possible Answers:

$40\sqrt2$

$160\sqrt2$

120

Correct answer:

$40\sqrt2$

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

$\text{Diagonal}^2=\text{side}^2+\text{side}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{20(\sqrt2)}{2}$

Simplify.

$\text{side}=10\sqrt2$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(10\sqrt2)$

Solve.

$\text{Perimeter}=40\sqrt2$

Report an Error

Example Question #485 : Quadrilaterals

Find the perimeter of a square inscribed in a circle that has a diameter of .

Possible Answers:

144

$24\sqrt2$

$36\sqrt2$

$48\sqrt2$

Correct answer:

$24\sqrt2$

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

$\text{Diagonal}^2=\text{side}^2+\text{side}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{12(\sqrt2)}{2}$

Simplify.

$\text{side}=6\sqrt2$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(6\sqrt2)$

Solve.

$\text{Perimeter}=24\sqrt2$

Report an Error

Example Question #486 : Quadrilaterals

Find the perimeter of a square inscribed in a circle that has a diameter of .

Possible Answers:

$35\sqrt2$

$42\sqrt2$

$28\sqrt2$

$14\sqrt2$

Correct answer:

$28\sqrt2$

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

$\text{Diagonal}^2=\text{side}^2+\text{side}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{14(\sqrt2)}{2}$

Simplify.

$\text{side}=7\sqrt2$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(7\sqrt2)$

Solve.

$\text{Perimeter}=28\sqrt2$

Report an Error

Example Question #487 : Quadrilaterals

Find the perimeter of a square inscribed in a circle that has a diameter of .

Possible Answers:

$24\sqrt2$

$16\sqrt2$

$32\sqrt2$

Correct answer:

$32\sqrt2$

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

$\text{Diagonal}^2=\text{side}^2+\text{side}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{16(\sqrt2)}{2}$

Simplify.

$\text{side}=8\sqrt2$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(8\sqrt2)$

Solve.

$\text{Perimeter}=32\sqrt2$

Report an Error

Example Question #488 : Quadrilaterals

Find the perimeter of a square inscribed in a circle that has a diameter of .

Possible Answers:

$8\sqrt2$

$4\sqrt2$

$10\sqrt2$

Correct answer:

$8\sqrt2$

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

$\text{Diagonal}^2=\text{side}^2+\text{side}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{4(\sqrt2)}{2}$

Simplify.

$\text{side}=2\sqrt2$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(2\sqrt2)$

Solve.

$\text{Perimeter}=8\sqrt2$

Report an Error

Example Question #489 : Quadrilaterals

Find the perimeter of a square inscribed in a circle that has a diameter of .

Possible Answers:

$24\sqrt2$

$12\sqrt2$

Correct answer:

$12\sqrt2$

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

$\text{Diagonal}^2=\text{side}^2+\text{side}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{6(\sqrt2)}{2}$

Simplify.

$\text{side}=3\sqrt2$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(3\sqrt2)$

Solve.

$\text{Perimeter}=12\sqrt2$

Report an Error

Example Question #891 : Basic Geometry

Find the perimeter of a square inscribed in a circle that has a diameter of .

Possible Answers:

$48\sqrt2$

$36\sqrt2$

Correct answer:

$36\sqrt2$

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

$\text{Diagonal}^2=\text{side}^2+\text{side}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{18(\sqrt2)}{2}$

Simplify.

$\text{side}=9\sqrt2$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(9\sqrt2)$

Solve.

$\text{Perimeter}=36\sqrt2$

Report an Error

Example Question #899 : Basic Geometry

Find the perimeter of a square inscribed in a circle that has a diameter of $14\sqrt3$ .

Possible Answers:

$28\sqrt5$

$28\sqrt2$

$28\sqrt6$

Correct answer:

$28\sqrt6$

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

$\text{Diagonal}^2=\text{side}^2+\text{side}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{14\sqrt3(\sqrt2)}{2}$

Simplify.

$\text{side}=7\sqrt6$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(7\sqrt6)$

Solve.

$\text{Perimeter}=28\sqrt6$

Report an Error

Example Question #900 : Basic Geometry

Find the perimeter of a square inscribed in a circle that has a diameter of 100 .

Possible Answers:

$400\sqrt2$

$200\sqrt2$

10000

$100\sqrt2$

Correct answer:

$200\sqrt2$

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

$\text{Diagonal}^2=\text{side}^2+\text{side}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{100(\sqrt2)}{2}$

Simplify.

$\text{side}=50\sqrt2$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(50\sqrt2)$

Solve.

$\text{Perimeter}=200\sqrt2$

Report an Error

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Basic Geometry : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #41 : How To Find The Perimeter Of A Square

Example Question #484 : Quadrilaterals

Example Question #485 : Quadrilaterals

Example Question #486 : Quadrilaterals

Example Question #487 : Quadrilaterals

Example Question #488 : Quadrilaterals

Example Question #489 : Quadrilaterals

Example Question #891 : Basic Geometry

Example Question #899 : Basic Geometry

Example Question #900 : Basic Geometry

All Basic Geometry Resources

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