What is the length of the leg of an isosceles right triangle if the hypotenuse is 12 units long?

In an isosceles right triangle, two sides equal

. Find the length of side

Possible Answers:

Correct answer:

Explanation:

This problem represents the definition of the side lengths of an isosceles right triangle. By definition the sides equal

, and

. However, if you did not remember this definition one can also find the length of the side using the Pythagorean theorem

ABCD is a square whose side is

units. Find the length of diagonal AC.

Possible Answers:

none of the other answers

Correct answer:

Explanation:

To find the length of the diagonal, given two sides of the square, we can create two equal triangles from the square. The diagonal line splits the right angles of the square in half, creating two triangles with the angles of

, and

degrees. This type of triangle is a special right triangle, with the relationship between the side opposite the

degree angles serving as x, and the side opposite the

degree angle serving as

Appyling this, if we plug

in for

we get that the side opposite the right angle (aka the diagonal) is

The area of a square is

. Find the length of the diagonal of the square.

Possible Answers:

Correct answer:

Explanation:

If the area of the square is

, we know that each side of the square is

, because the area of a square is

Then, the diagonal creates two

special right triangles. Knowing that the sides =

, we can find that the hypotenuse (aka diagonal) is

An isosceles right triangle has a hypotenuse of

. Find its area.

Possible Answers:

Not enough information to solve

Correct answer:

Explanation:

In order to calculate the triangle's area, we need to find the lengths of its legs. An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as

triangles and their side lengths follow a specific pattern that states that one can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2.

Now we can calculate the area using the formula

Now, convert to feet.

The base of a right isosceles triangle is 8 inches. The hypotenuse is not the base. What is the area of the triangle in inches?

Possible Answers:

Correct answer:

Explanation:

To find the area of a triangle, multiply the base by the height, then divide by 2. Since the short legs of an isosceles triangle are the same length, we need to know only one to know the other. Since, a short side serves as the base of the triangle, the other short side tells us the height.

The hypotenuse of an isosceles right triangle has a measure of

. Find its perimeter.

Possible Answers:

Not enough information to solve

Correct answer:

Explanation:

In order to calculate the triangle's perimeter, we need to find the lengths of its legs. An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as

Now we can calculate the perimeter by doubling

and adding

The side lengths of an isoceles right triangle measure

. Find its perimeter.

Possible Answers:

Not enough information to solve

Correct answer:

Explanation:

An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as

triangles and their side lenghts follow a specific pattern that states you can calculate the length of the hypotenuse of an isoceles triangle by multiplying the length of one of the legs by the square root of 2.

Now we can calculate the perimeter by doubling

and adding

A triangle has two angles equal to

and two sides equal to

. What is the perimeter of this triangle?

Possible Answers:

Correct answer:

Explanation:

When a triangle has two angles equal to

, it must be a

isosceles right triangle.

The pattern for the sides of a

Since two sides are equal to

, this triangle will have sides of

Add them all together to get

An isosceles triangle has a base of 6 and a height of 4. What is the perimeter of the triangle?

Possible Answers:

Correct answer:

Explanation:

An isosceles triangle is basically two right triangles stuck together. The isosceles triangle has a base of 6, which means that from the midpoint of the base to one of the angles, the length is 3. Now, you have a right triangle with a base of 3 and a height of 4. The hypotenuse of this right triangle, which is one of the two congruent sides of the isosceles triangle, is 5 units long (according to the Pythagorean Theorem).

The total perimeter will be the length of the base (6) plus the length of the hypotenuse of each right triangle (5).

5 + 5 + 6 = 16

What is the area of a square that has a diagonal whose endpoints in the coordinate plane are located at (-8, 6) and (2, -4)?

Possible Answers:

Explanation:

Andrea
Certified Tutor

University of York, Bachelor of Science, Genetics.

Tracey
Certified Tutor

Arkansas State University-Main Campus, Bachelor of Science, Elementary School Teaching. University of Phoenix-Phoenix-Hohokam...

Nidhi
Certified Tutor

Georgia Institute of Technology-Main Campus, Bachelor of Science, Psychology.

If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC 101 S. Hanley Rd, Suite 300 St. Louis, MO 63105

Or fill out the form below: