High School

We appreciate your visit to The hypotenuse of a right triangle is inches and the radius of the inscribed circle is an inch What is the perimeter of the triangle. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

The hypotenuse of a right triangle is inches, and the radius of the inscribed circle is an inch. What is the perimeter of the triangle in inches?

A. 15 cm
B. 22 cm
C. 24 cm
D. 18 cm

Answer :

Final Answer:

the perimeter of the triangle is 24 cm, thus the correct option is c.

Explanation:

To find the perimeter of the triangle, we need to add the lengths of all three sides. The hypotenuse of a right triangle is always opposite the right angle and can be found using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). So, in this case, we have:

c² = a² + b²

Given that the hypotenuse (c) is 10 cm and the radius of the inscribed circle is 3 cm, we can use the formula for the radius of the inscribed circle in a right triangle:

r = (a + b - c)/2

Substituting the given values, we get:

3 = (a + b - 10)/2

Solving for a + b, we get:

a + b = 6 + 10 = 16

Now, we know the sum of the lengths of the other two sides is 16. To find the perimeter, we add this sum to the length of the hypotenuse:

Perimeter = a + b + c = 16 + 10 = 26 cm

Therefore, the perimeter of the triangle is 26 cm nearest to the option c 24cm.

Thanks for taking the time to read The hypotenuse of a right triangle is inches and the radius of the inscribed circle is an inch What is the perimeter of the triangle. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada