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Basic Geometry : How to find the length of the hypotenuse of a 45/45/90 right isosceles triangle : Pythagorean Theorem

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Example Question #21 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

Find the length of the hypotenuse.

Possible Answers:

$2\sqrt2$

$4\sqrt3$

$4\sqrt2$

Correct answer:

$4\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

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

Now, plug in the values of and from the question.

$\text{Hypotenuse}=\sqrt{4^2+4^2}$

$\text{Hypotenuse}=\sqrt{16+16}$

Solve.

$\text{Hypotenuse}=\sqrt{32}$

Simplify.

$\text{Hypotenuse}=4\sqrt2$

Report an Error

Example Question #21 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

A right isosceles triangle has leg lengths of $\frac{1}{2}$ . What is the length of the hypotenuse?

Possible Answers:

$\frac{\sqrt2}{4}$

$\frac{\sqrt2}{2}$

$2\sqrt2$

$4\sqrt2$

Correct answer:

$\frac{\sqrt2}{2}$

Explanation:

Recall the Pythagorean Theorem:

a^2+b^2=c^2

Since we know that this is an isosceles right triangle, we know the following:

a=b

The Pythagorean Theorem can then be simplifed to the following equation:

a^2+a^2=2a^2=c^2

Now, solve for since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$

$c=a\sqrt2$

Now, plug in the given value for to find the length of the hypotenuse.

$c=\frac{\sqrt2}{2}$

Report an Error

Example Question #23 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

A right isosceles triangle has leg lengths of $\frac{1}{3}$ . What is the length of the hypotenuse?

Possible Answers:

$3\sqrt2$

$\frac{\sqrt3}{3}$

$\frac{\sqrt2}{9}$

$\frac{\sqrt2}{3}$

Correct answer:

$\frac{\sqrt2}{3}$

Explanation:

Recall the Pythagorean Theorem:

a^2+b^2=c^2

Since we know that this is an isosceles right triangle, we know the following:

a=b

The Pythagorean Theorem can then be simplifed to the following equation:

a^2+a^2=2a^2=c^2

Now, solve for since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$

$c=a\sqrt2$

Now, plug in the given value for to find the length of the hypotenuse.

$c=\frac{\sqrt2}{3}$

Report an Error

Example Question #24 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

A right isosceles triangle has leg lengths of $\frac{1}{5}$ . What is the length of the hypotenuse?

Possible Answers:

$\frac{\sqrt5}{2}$

$5\sqrt2$

$\frac{\sqrt2}{5}$

$\frac{1}{5}$

Correct answer:

$\frac{\sqrt2}{5}$

Explanation:

Recall the Pythagorean Theorem:

a^2+b^2=c^2

Since we know that this is an isosceles right triangle, we know the following:

a=b

The Pythagorean Theorem can then be simplifed to the following equation:

a^2+a^2=2a^2=c^2

Now, solve for since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$

$c=a\sqrt2$

Now, plug in the given value for to find the length of the hypotenuse.

$c=\frac{\sqrt2}{5}$

Report an Error

Example Question #25 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

A right isosceles triangle has leg lengths of . In terms of , what is the length of the hypotenuse?

Possible Answers:

x^2

$x\sqrt2$

$\frac{x\sqrt2}{2}$

$\sqrt{2x}$

Correct answer:

$x\sqrt2$

Explanation:

Recall the Pythagorean Theorem:

a^2+b^2=c^2

Since we know that this is an isosceles right triangle, we know the following:

a=b

The Pythagorean Theorem can then be simplifed to the following equation:

a^2+a^2=2a^2=c^2

Now, solve for since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$

$c=a\sqrt2$

Now, plug in the given value for to find the length of the hypotenuse.

$c=x\sqrt2$

Report an Error

Example Question #26 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

A right isosceles triangle has leg lengths of $\frac{3}{4}$ . What is the length of the hypotenuse?

Possible Answers:

$\frac{3\sqrt2}{4}$

$\frac{2\sqrt2}{3}$

$\frac{4\sqrt3}{3}$

$\frac{\sqrt2}{6}$

Correct answer:

$\frac{3\sqrt2}{4}$

Explanation:

Recall the Pythagorean Theorem:

a^2+b^2=c^2

Since we know that this is an isosceles right triangle, we know the following:

a=b

The Pythagorean Theorem can then be simplifed to the following equation:

a^2+a^2=2a^2=c^2

Now, solve for since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$

$c=a\sqrt2$

Now, plug in the given value for to find the length of the hypotenuse.

$c=\frac{3\sqrt2}{4}$

Report an Error

Example Question #27 : Triangles

A right isosceles triangle has leg lengths of $\frac{1}{8}$ . What is the length of the hypotenuse?

Possible Answers:

$\frac{\sqrt2}{8}$

$8\sqrt2$

$4\sqrt2$

$12\sqrt2$

Correct answer:

$\frac{\sqrt2}{8}$

Explanation:

Recall the Pythagorean Theorem:

a^2+b^2=c^2

Since we know that this is an isosceles right triangle, we know the following:

a=b

The Pythagorean Theorem can then be simplifed to the following equation:

a^2+a^2=2a^2=c^2

Now, solve for since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$

$c=a\sqrt2$

Now, plug in the given value for to find the length of the hypotenuse.

$c=\frac{\sqrt2}{8}$

Report an Error

Example Question #27 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

A right isosceles triangle has leg lengths of $4\sqrt3$ . What is the length of the hypotenuse?

Possible Answers:

$8\sqrt3$

$6\sqrt2$

$4\sqrt6$

$9\sqrt5$

Correct answer:

$4\sqrt6$

Explanation:

Recall the Pythagorean Theorem:

a^2+b^2=c^2

Since we know that this is an isosceles right triangle, we know the following:

a=b

The Pythagorean Theorem can then be simplifed to the following equation:

a^2+a^2=2a^2=c^2

Now, solve for since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$

$c=a\sqrt2$

Now, plug in the given value for to find the length of the hypotenuse.

$c=(4\sqrt3)(\sqrt2)$

Simplify.

$c=4\sqrt6$

Report an Error

Example Question #28 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

A right isosceles triangle has leg lengths of $\sqrt2$ . What is the length of the hypotenuse?

Possible Answers:

Correct answer:

Explanation:

Recall the Pythagorean Theorem:

a^2+b^2=c^2

Since we know that this is an isosceles right triangle, we know the following:

a=b

The Pythagorean Theorem can then be simplifed to the following equation:

a^2+a^2=2a^2=c^2

Now, solve for since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$

$c=a\sqrt2$

Now, plug in the given value for to find the length of the hypotenuse.

$c=(\sqrt2)(\sqrt2)$

Simplify.

c=2

Report an Error

Example Question #29 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

A right isosceles triangle has leg lengths of $\sqrt3$ . What is the length of the hypotenuse?

Possible Answers:

$\sqrt6$

$\sqrt2$

$\sqrt5$

$3\sqrt2$

Correct answer:

$\sqrt6$

Explanation:

Recall the Pythagorean Theorem:

a^2+b^2=c^2

Since we know that this is an isosceles right triangle, we know the following:

a=b

The Pythagorean Theorem can then be simplifed to the following equation:

a^2+a^2=2a^2=c^2

Now, solve for since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$

$c=a\sqrt2$

Now, plug in the given value for to find the length of the hypotenuse.

$c=(\sqrt3)(\sqrt2)$

Simplify.

$c=\sqrt6$

Report an Error

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Basic Geometry : How to find the length of the hypotenuse of a 45/45/90 right isosceles triangle : Pythagorean Theorem

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #21 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

Example Question #21 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

Example Question #23 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

Example Question #24 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

Example Question #25 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

Example Question #26 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

Example Question #27 : Triangles

Example Question #27 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

Example Question #28 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

Example Question #29 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

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