IPM Question Paper 2019 | IPM Rohtak Quantitative Aptitude

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Question 31 : A circle is inscribed in an equilateral triangle of side 24 cm, touching its sides. What is the area of
the remaining portion of the triangle?

1. 144√3 - 48π cm²
2. 121√3 - 36π cm²
3. 144√3 - 36π cm²
4. 121√3 - 48π cm²

Explanatory Answer

When a circle is inscribed in an equilateral triangle, the radius of the circle will be \\frac{1}{3}\\) rd of the height of the triangle.

Height of an equilateral triangle(h) = \\frac{√3}{2}\\) * a
(where a is the length of a side of the equilateral triangle)

h = √\\frac{√3}{2}\\) * 24 = 12 √3.

Radius of the Circle(r) = \\frac{1}{3}\\) * h = 12 \\frac{√3}{3}\\) = 4 √3.

Area of an equilateral triangle (A) = \\frac{√3}{4}\\) * a²
(where a is the length of a side of the equilateral triangle)

A = \\frac{√3}{4}\\) * (24)² = √3 * 144.

Area of the Circle (a) = π r².
(where r is the radius of the circle)

a = π (4 √3)² = 48 π.

Area of the remaining portion of the triangle= A – a = √3 * 144 - 48 π

Area of the remaining portion of the triangle= 144 √3 - 48 π.

The question is "A circle is inscribed in an equilateral triangle of side 24 cm, touching its sides. What is the area of
the remaining portion of the triangle?"

Hence, the answer is 144√3 - 48π cm²

Choice A is the correct answer

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