Question

Pythagorean Theorem

Determine which set of side measurements could be used to form a right triangle.

A. 5, 12, 13
B. 7, 15, 20
C. 5, 8, 14
D. 6, 7, 8

Answer 1

Explanation:

Pythagorean theorem c^2 = a^2 + b^2

this is for right triangles and 'c' is the longest side

A 13^2 = 5^2 + 12 ^2 ??? Yes

B no

C no

D no

Answer 2

The Pythagorean Theorem states that for a right triangle, the sum of the squares of the lengths of the legs (the sides adjacent to the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle). Using this theorem, we can determine which set of side measurements could be used to form a right triangle:

A. 5, 12, 13: This set of side measurements satisfies the Pythagorean Theorem since 5^2 + 12^2 = 13^2. Therefore, this set of side measurements could be used to form a right triangle.

B. 7, 15, 20: This set of side measurements does not satisfy the Pythagorean Theorem since 7^2 + 15^2 is not equal to 20^2. Therefore, this set of side measurements could not be used to form a right triangle.

C. 5, 8, 14: This set of side measurements does not satisfy the Pythagorean Theorem since 5^2 + 8^2 is not equal to 14^2. Therefore, this set of side measurements could not be used to form a right triangle.

D. 6, 7, 8: This set of side measurements satisfies the Pythagorean Theorem since 6^2 + 7^2 = 8^2. Therefore, this set of side measurements could be used to form a right triangle.

Therefore, sets A and D are the sets of side measurements that could be used to form right triangles.