# The area of a right-angled isosceles triangle is 4.5 cm, find the radius of the inscribed circle.

September 28, 2021 | education

| Since triangle ABC is rectangular, its area will be equal to:

Savs = AB * AC / 2, and since the triangle and isosceles, AB = AC, then

Savs = AB ^ 2/2 = 4.5 cm2.

AB ^ 2 = 2 * 4.5 = 9 cm2.

AB = 3 cm.

By the Pythagorean theorem, we determine the length of the BC hypotenuse.

BC ^ 2 = AB ^ 2 + AC ^ 2 = 3 ^ 2 + 3 ^ 2 = 9 + 9 = 18.

BC = √18 = 3 * √2 cm.

Based on three dimensions of the triangle, we determine the radius of the circle inscribed in it.

R = (AB + AC – BC / 2 = (3 + 3 – 3 * √2) / 2 = (6 – 3 * √2) / 2 = 3 – 1.5 * √2 cm.

Answer: The radius of the inscribed circle is 3 – 1.5 * √2 cm.

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