Question

1. Which of the following measurements could be the three side lengths of a right triangle? a. 4 cm, 5 cm, 9 cm b. 12 cm, 20 cm, 25 cm c. 18 cm, 24 cm, 30 cm d. 2 cm, 3 cm, 5 cm

Answer 1

Answer:

b and c

Step-by-step explanation:

The Triangle Inequality Theorem lets us know that the sum of the two shortest sides of the triangle must be greater than the third side of the triangle.

In both A and D, the sum of the shortest two sides are equal to, not greater than the third side, so they will not form a triangle.

In B, 12+20 is 32, which is greater than 25. And in C, 18+24 is 42, which is greater than 30, so they both will form a triangle.

Answer 2

Using the Pythagorean Theorem, it is found that possible side lengths of a right triangle are given by:

c. 18 cm, 24 cm, 30 cm

What is the Pythagorean Theorem?

The Pythagorean Theorem relates the length of the legs $l_1$ and $l_2$ of a right triangle with the length of the hypotenuse h, according to the following equation:

$h^2 = l_1^2 + l_2^2$

The length of the hypotenuse is always greater than the length of the legs. The Pythagorean Theorem has to hold true, which holds only for option C, as:

18² + 24² = 30²

900 = 900

More can be learned about the Pythagorean Theorem at https://brainly.com/question/654982

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