The radius of a circle circumscribed about a right-angled triangle is 5 cm, and one of the legs is 8 cm.
| February 4, 2021 | education
The radius of a circle circumscribed about a right-angled triangle is 5 cm, and one of the legs is 8 cm. Find the perimeter of the triangle.
Since in any right-angled triangle the radius of the circumscribed circle is equal to half the length of the hypotenuse of this right-angled triangle, the length of the hypotenuse of this right-angled triangle is 5 * 2 = 10 cm.
According to the condition of the problem, one of the legs of this right-angled triangle is 8 cm.
Using the Pythagorean theorem, we find the length of the second leg of this triangle:
√ (10 ^ 2 – 8 ^ 2) = √ (100 – 64) = √36 = 6 cm.
Knowing the lengths of all sides of the triangle, we find its perimeter:
6 + 8 + 10 = 14 + 10 = 24 cm.
Answer: 24 cm.
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