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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