The legs of a right-angled triangle are 7 cm and 24 cm.

| September 19, 2021 | education

The legs of a right-angled triangle are 7 cm and 24 cm. Calculate: – the radius of the circumscribed circle; is the radius of the inscribed circle. R = cm; r = cm

Let’s find out what the hypotenuse should be in our triangle, when from the condition of the problem we know that the lengths of the legs of this triangle are 7 and 24 centimeters:

√ (7 ^ 2 + 24 ^ 2) = √ (49 + 576) = √625 = 25.

Let’s find out what then the radius of the circumscribed circle will be, because we know that it corresponds to half of the hypotenuse:

25: 2 = 12.5.

Let’s find out what then the radius of the inscribed circle will be:

(7 + 24 – 25): 2 = 3.

Answer: Under such initial conditions, the radius of the inscribed will be equal to 3 cm, and the radius of the described one will be 12.5 cm.



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