Question

Which of the following sets of numbers could represent the three sides of a right

triangle?
A. {11, 59, 61}
B. {28, 45,54}
C. {20, 21, 30}
D. {10, 24, 26}

Answer 1

Answer: D. {10, 24, 26}

Explanation

We plug each triple into the Pythagorean theorem.

Let's try choice A.

a^2 + b^2 = c^2

11^2 + 59^2 = 61^2

121 + 3481 = 3721

3602 = 3721

The last equation is false, so choice A is not a right triangle.

Similar situations happen with choices B and C.

We cross choices A, B, and C off the list.

Choice D on the other hand is a right triangle because of this scratch work shown here.

a^2 + b^2 = c^2

10^2 + 24^2 = 26^2

100 + 576 = 676

676 = 676

We arrive at a true statement, so the first equation is true when (a,b,c) = (10,24,26). This is one of the infinitely many Pythagorean triples. It is based on the Pythagorean triple (5,12,13). Double each value of (5,12,13) to end up with (10,24,26).

Answer 2

To determine if a set of numbers can represent the three sides of a right triangle, we need to check if the Pythagorean theorem holds true. Only sets C and D satisfy the Pythagorean theorem, so they could represent the three sides of a right triangle.

Step-by-step explanation:

A right triangle is a triangle that has one angle equal to 90 degrees.

To determine if a set of numbers can represent the three sides of a right triangle, we need to check if the Pythagorean theorem holds true.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's check each set of numbers:

• A. {11, 59, 61}: 11^2 + 59^2 = 3602 ≠ 61^2
• B. {28, 45, 54}: 28^2 + 45^2 = 3749 ≠ 54^2
• C. {20, 21, 30}: 20^2 + 21^2 = 841 = 30^2
• D. {10, 24, 26}: 10^2 + 24^2 = 676 = 26^2

Only set C and set D satisfy the Pythagorean theorem, so these are the sets of numbers that could represent the three sides of a right triangle.