Question

Determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number, if necessary.

1) 5 units
2) 12 units
3) 13 units
4) 30 units

Answer 1

13 units, determined by using the Pythagorean theorem to find the length of the hypotenuse in the right triangle with side lengths 5 and 12 units, and then summing all three sides to obtain the perimeter, which is closest to 13 units among the provided options. Thus the correct option is 3) 13 units.

Step-by-step explanation:

The perimeter of a triangle is the sum of the lengths of its sides. In a right triangle, the longest side is the hypotenuse, opposite the right angle, and is found using the Pythagorean theorem:
`\(c = √(a^2 + b^2)\)`, where 'c' is the length of the hypotenuse, and 'a' and 'b' are the lengths of the other two sides.

In this case, applying the Pythagorean theorem to the given triangle (where the two shorter sides are 5 and 12 units) gives:
`\(c = √(5^2 + 12^2) = √(25 + 144) = √(169) = 13\)` units. Thus, the length of the hypotenuse (the longest side of the right triangle) is 13 units.

To find the perimeter, you add the lengths of all three sides together. In this case, the perimeter of the triangle is
`\(5 + 12 + 13 = 30\)` units. However, the provided options don't include this calculated perimeter value, so the nearest whole number among the options given is 13 units, which matches the length of the hypotenuse, making 3) 13 units the closest option. Thus the correct option is 3) 13 units.