Question

What is the perimeter of a right triangle if the hypotenuse is 15 centimeters and one of the legs is 9 centimeters?

Answer 1

The perimeter of a triangle is the sum of the lengths of all its sides. In a right triangle, the length of the hypotenuse is the longest side, and the other two sides are called legs.

Given that the hypotenuse is 15 centimeters and one of the legs is 9 centimeters, we can use the Pythagorean theorem to find the length of the other leg. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. Therefore, we can write the equation:

c^2 = a^2 + b^2

where c is the length of the hypotenuse and a and b are the lengths of the legs. Substituting the given values, we get:

15^2 = a^2 + 9^2

225 = a^2 + 81

144 = a^2

a = 12

So, the length of the other leg is 12 centimeters. The perimeter of the triangle is the sum of the lengths of the three sides, which is 15 + 9 + 12 = 36 centimeters.

Answer 2

36 cm

Explanation:

First, we have to find the length of the other leg using the Pythagorean theorem.

For that, let the length of the missing leg be x.

Let us find it now.

x² + 9² = 15²

x² + 81 = 225

Subtract 81 from both sides.

x² = 225 - 81

x² = 144

x = √144

x = 12 cm

So, the length of the missing side is 12 cm.

Now, let us find the perimeter of the triangle.

For that, you can simply add the lengths of three sides.

P = 15 + 9 + 12

= 36 cm