1.  The ratio of the areas of the incircle and circumcircle of an equilateral triangle is :

1 : 2
1 : 3
1 : 4
1 : 9

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Answer: Option  C Explanation:Radius of incircle of an equilateral triangle = a⁄2$\sqrt{3}$
Radius of circumcircle of an equilateral triangle = a⁄$\sqrt{3}$
Required ratioπa2⁄12 : πa2⁄3 = 1⁄12 = 1⁄3 = 1 : 4. ```

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2.  The sides of a triangle are in the ratio of 12 : 13 : 14. If the perimeter is 52 cm, then the length of the smallest side is :

9 cm
10 cm
11 cm
12 cm

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Answer: Option  D Explanation:Ratio of sides = 1⁄2 : 1⁄3 : 1⁄4 = 6 : 4 : 3
Perimeter   = (52 * 6⁄13 ) cm, (52 * ⁄13) cm and ( 52 * 3⁄13) cm.
a = 24 cm, b = 16 cm, c= 12 cm.
Length of smallest side = 12 cm. ```

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3.  The perimeter of a right-angled triangle is 60 cm. Its hypotenuse is 26 cm. The area of the triangle is :

120 cm2
240 cm2
390 cm2
780 cm2

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Answer: Option  A Explanation:Let Base = b cm and Height = h cm.
b + h + 26 = 60.
b + h = 34.
(b + h)2 = (34)2.
Also, b2 + h2 = (26)2.
(b + h)2 - (b2 + h2) = (34)2 - (26)2
2bh = (34 + 26) (34 - 26) = 480.
bh = 240 = 1⁄2 bh = 120. ```

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4.  If the area of an equilateral triangle is 24$\sqrt{3}$ sq. cm, then its perimeter is :

2$\sqrt{6}$ cm
4$\sqrt{6}$ cm
12$\sqrt{6}$ cm
96 cm

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Answer: Option  C Explanation:Area of an equilateral triangle of side a cm = ($\sqrt{3}$⁄4 a2) cm2.
$\sqrt{3}$⁄4 a2 = 24$\sqrt{3}$.
a2 = 96.
a  = 4$\sqrt{6}$.
Perimeter = 3a = 12$\sqrt{6}$cm. ```

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5.  In two triangles, the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4. Find the ratio of their bases.

4 : 5
4 : 9
16 : 5
16 : 9

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Answer: Option  D Explanation:Let the base of the two triangles be x and y and their heights be 3h and 4h respectively. Then
1⁄2 * x * 3h⁄1⁄2 * y * 4h = 4⁄3.
x⁄y = (4⁄3 * 4⁄3) = 16⁄9.
Required ratio = 16 : 9. ```

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