The hypotenuse of a right triangle is 16, and the radius of the inscribed circle of this triangle is 3.
| April 6, 2021 | education
The hypotenuse of a right triangle is 16, and the radius of the inscribed circle of this triangle is 3. Find the perimeter of the triangle.
Immediately recall the formula for the radius of the inscribed circle in a right-angled triangle.
r = (a + b – c) / 2 – a and b – legs, c – hypotenuse.
Substitute the known values of the radius and hypotenuse.
3 = (a + b – 16) / 2.
6 = a + b – 16.
6 + 16 = a + b.
22 = a + b.
The perimeter is the sum of all sides of the triangle.
a + b + c = 22 + 16 = 38 cm.
Answer: P = 38 cm.
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