1.  The area of the largest triangle that can be inscribed in a semi-circle of radius r, is :

r2
2r2
r3
2r3

Answer

Option

Required area = 12 * base * height = (12 * 2r * r) = r2.

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2.  An equilateral triangle, a square and a circle have equal perimeters. If T denotes the area of the triangles, S the area of the square and C, the area of the circle, then :

S < T < C
T < C < S
T < S < C
C < S < T

Answer

Option

Let the perimeter of each be a. Then, side of the equilateral triangle = a3; side of the square = a4 radius of the circle = a. T = $\sqrt{3}$4 * (a3)2 = $\sqrt{3}$a236; S = (a4)2 = a216; C = π * (a)2 = a2 = 7a288. So, C > S > T.

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3.  Formula for a Radius of incircle of an equilateral triangle of side a ?

a2$\sqrt{2}$
a2$\sqrt{3}$
a3$\sqrt{2}$
a3$\sqrt{3}$

Answer

Option

No answer description available for this question.

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4.  Formula for area of a equilateral triangle

$\sqrt{3}$4 * (side)2
$\sqrt{2}$4 * (side)2
$\sqrt{3}$4 * (side)3
$\sqrt{3}$2 * (side)2

Answer

Option

No answer description available for this question.

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5.  The sides of a triangle are 6 cm, 11 cm and 15 cm. The radius of its incircle is :

3$\sqrt{2}$ cm
4$\sqrt{2}$5 cm
5$\sqrt{2}$4 cm
6$\sqrt{2}$

Answer

Option

We have : a = 6, b = 11, c = 15, s = 12(6 + 11 + 15) = 16. Area of the triangle , △ = $\sqrt{\mathrm{16 * 10 * 5 * 1}}$ = 20$\sqrt{2}$ cm2. Radius of incircle =s = 20$\sqrt{2}$16 = 5$\sqrt{2}$4

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