Understanding the Pythagorean Theorem

Solve each of these problems.

Question 1

Short answer

A right triangle has one leg that measures 6 units and a hypotenuse that measures 10 units. What is the length of the other leg?

Question 2

Short answer

If a right triangle has legs of lengths 8 units and 15 units, what is the length of the hypotenuse?

Question 3

Short answer

The lengths of the legs of a right triangle are represented by x and y, and the length of the hypotenuse is represented by z. Write the Pythagorean Theorem using these variables.

Question 4

Short answer

A ladder is leaning against a wall, reaching a height of 12 feet. If the base of the ladder is 5 feet away from the wall, how long is the ladder?

Math

8th grade

Unit

Triangles and The Pythagorean Theorem

Topic

7.3 Pythagorean Theorem

Format

Short answer

Short answer rubric

Pythagorean Theorem

· Correct answers must calculate the missing leg as 8 units when one leg is 6 units and the hypotenuse is 10 units using the Pythagorean Theorem.
· Correct answers must calculate the missing leg as approximately 12.7 units when one leg is 8 units and the hypotenuse is 15 units using the Pythagorean Theorem.
· Correct answers must represent the Pythagorean Theorem as x^2 + y^2 = z^2, where x and y are the lengths of the legs and z is the length of the hypotenuse.
· Correct answers must calculate the length of the ladder as 13 feet when the height reached is 12 feet and the base is 5 feet from the wall using the Pythagorean Theorem.

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