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?

Algebra.Com
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): You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~

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.

----------------

Regarding formula  (1)  and its proof,  see the lesson

    - The radius of a circle inscribed into a right angled triangle

in this site.



RELATED QUESTIONS

A circle is inscribed in an equilateral triangle. If the circumference of the circle is... (answered by josgarithmetic)
If a right triangle has legs of 6 cm and 8 cm, then the hypotenuse is... (answered by nerdybill)
an isosceles right triangle is inscribed in a circle. Find the radius of the circle if... (answered by ikleyn)
A right triangle having a 32.5 degree angle is inscribed in a circle with radius 42.5 cm. (answered by Alan3354)
A right angled triangle has a perimeter of 120 cm. If the hypotenuse is 50 cm, what is... (answered by unlockmath)
A right triangle is inscribed in a circle with radius 26 cm. If the length of one of the... (answered by ikleyn)
Find the area of the inscribed circle of a triangle, where the triangle has an area of... (answered by ikleyn)
Find the area of the largest right triangle that can be inscribed in a circle of radius... (answered by ikleyn)
What is the hypotenuse of a right triangle that has legs measuring 6 cm and 8... (answered by chessace)