SOLUTION: A circle is inscribed in a right triangle that has a hypotenuse of 182 cm. If the perimeter of the triangle is 420 cm, what is the radius of the inscribed circle?
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Question 1190317: A circle is inscribed in a right triangle that has a hypotenuse of 182 cm. If the perimeter of the triangle is 420 cm, what is the radius of the inscribed circle? Answer by ikleyn(52797) (Show Source):
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A circle is inscribed in a right triangle that has a hypotenuse of 182 cm.
If the perimeter of the triangle is 420 cm, what is the radius of the inscribed circle?
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For any right triangle, the radius of the inscribed circle is
r = , (1)
where "a" and "b" are the legs lengths and "c" is the hypotenuse length.
We are given the perimeter P = a + b + c = 420 cm and the hypotenuse length c= 182 cm,
therefore, we can easily compute the radius of the inscribed circle
r = = = = 210 - 182 = 28 centimeters. ANSWER
Solved.
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Regarding formula (1) and its proof, see the lesson
