The height drawn to the base of the isosceles triangle is 9cm, and the base itself is 24cm.

| August 3, 2021 | education

The height drawn to the base of the isosceles triangle is 9cm, and the base itself is 24cm. Find the radius of the circle inscribed in the triangle?

We will draw from the top B to the height BH, to the base of the AC.

Since, by condition, the triangle is isosceles, then its height BH is the median of the triangle and divides its base AC in half, AH = CH = AC / 2 = 24/2 = 12 cm.

In a right-angled triangle ABH, by the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = BH ^ 2 + AH ^ 2 = 9 ^ 2 + 12 ^ 2 = 81 + 144 = 225.

AB = 15 cm.

Determine the area of ​​the triangle ABC.

Savs = AC * BH / 2 = 24 * 9/2 = 108 cm.

Let’s define the semiperimeter of the triangle ABC.

p = (AB + BC + AC) / 2 = (15 + 15 + 24) / 2 = 27 cm.

Determine the radius of the inscribed circle.

r = S / p = 108/27 = 4 cm.

Answer: The radius of the inscribed circle is 4 cm.



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