# IPM Sample Paper 2020 | IPM Rohtak Quantitative Aptitude

###### IPMAT Sample Paper | IPMAT Question Paper | Question 31

IPMAT 2020 Sample Paper IPM Rohtak Quantitative Aptitude. Solve questions from IPMAT 2020 Sample Paper from IPM Rohtak and check the solutions to get adequate practice. The best way to ace IPMAT is by solving IPMAT Question Paper. To solve other IPMAT Sample papers, go here: IPM Sample Paper

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

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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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