Question

Which of these four sets of side lengths will form a right triangle?

Set 1:
a) 3, 4, 5
b) 1, 1, 2
c) 5, 12, 13
d) 6, 8, 10

Set 2:
a) 7, 24, 25
b) 2, 2, 5
c) 8, 15, 17
d) 4, 5, 6

Set 3:
a) 1, 2, 2.5
b) 3, 5, 7
c) 10, 11, 12
d) 9, 12, 15

Set 4:
a) 8, 15, 16
b) 5, 5, 5
c) 9, 40, 41
d) 12, 16, 20

Answer 1

Sets 1 (3, 4, 5) and Set 4 (12, 16, 20) will form a right triangle.

Step-by-step explanation:

The sets that form a right triangle are Set 1: a) 3, 4, 5, and Set 4: d) 12, 16, 20.

To determine if a set of side lengths forms a right triangle, we can use the Pythagorean theorem. 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.

For Set 1: a² + b² = c², where a = 3, b = 4, and c = 5. 3² + 4² = 9 + 16 = 25 which is equal to 5². So, Set 1 forms a right triangle.

For Set 4: a² + b² = c², where a = 12, b = 16, and c = 20. 12² + 16² = 144 + 256 = 400 which is equal to 20². So, Set 4 forms a right triangle.