1). The sides of a triangle area in the ratio of \( \Large \frac{1}{3}:\frac{1}{4}:\frac{1}{5} \) and its perimeter is 94 Cm.Find the length of the smallest side of the triangle.
A). 18 cm |
B). 22.5 cm |
C). 24 m |
D). 27 cm |
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2). The area of an equilateral triangle is \( \Large \Large 4\sqrt{3} \)sq cm. Find the length of each side of the triangle
A). 3 cm |
B). \( \Large 2\sqrt{2} \)cm |
C). \( \Large 2\sqrt{3} \)cm |
D). 4 cm |
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3). The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle?
A). \( \Large 6cm^{2} \) |
B). \( \Large 8cm^{2} \) |
C). \( \Large 10cm^{2} \) |
D). \( \Large 12cm^{2} \) |
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4). If the area of an equilateral triangle is x and its perimeter is y. then which one of the following is correct?
A). \( \Large y^{4}=432x^{2} \) |
B). \( \Large y^{4}=216x^{2} \) |
C). \( \Large y^{2}=432x^{2} \) |
D). None of these |
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5). The area of an isosceles \( \Large \triangle ABC \) with AB = AC and altitude AD = 3 cm is 12 sq cm. What is its perimeter?
A). 18 cm |
B). 16 cm |
C). 14 cm |
D). 12 cm |
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6). The area of an equilateral triangle is \( \Large \Large \frac{\sqrt{243}}{4} \)sq cm. Find the length of its side.
A). 3 cm |
B). \( \Large 3\sqrt{3} \)cm |
C). 9 cm |
D). \( \Large \sqrt{3} \)cm |
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7). The ratio of length of each equal side and the third side of an isosceles triangle is 3:4. If the area of the triangle is \( \Large \Large 18\sqrt{5} \) sq units, the third side is
A). \( \Large 8\sqrt{2} \)units |
B). 12 units |
C). 16 units |
D). \( \Large 5\sqrt{10} \)units |
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8). Three sides of a triangular field are of length 15 m, 20 m and 25 m long, respectively. Find the cost of sowing seeds in the field at the rate of RS. 5 per Sq m.
A). 750 |
B). 150 |
C). 300 |
D). 600 |
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9). A \( \Large \Large \triangle DEF \) is formed by joining the mid points of the sides of \( \Large \Large \triangle ABC\). Similarly, a \( \Large \Large \triangle PQR \) is formed by joining the mid-points of the sides of the \( \Large \Large \triangle DEF \). If the sides of the PQR are of lengths 1, 2 and 3 units, what is the perimeter of the \( \Large \Large \triangle ABC \)?
A). 18 units |
B). 24 units |
C). 48 units |
D). Cannot be determined |
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10). Find the area of a rectangle having 15 m length and 8 m breadth.
A). 120 sq m |
B). 111 sq m |
C). 115 sq m |
D). 125 sq m |
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A) \( \Large 6\sqrt{3} \)cm

B) \( \Large 2\sqrt{3} \)cm

C) \( \Large 5\sqrt{3} \)cm

D) \( \Large 7\sqrt{3} \)cm

Correct Answer:

Description for Correct answerAccording to the question,

\( \Large \frac{\sqrt{3}}{4}a^{2}= 3\sqrt{3} \)

=> \( \Large \frac{1}{4}a^{2} \)=3 => \( \Large a^{2}=3\times 4 \)

a=\( \Large 2\sqrt{3} \)

Required perimeter=3a=\( \Large 3\times 2\sqrt{3} \)

=\( \Large 6\sqrt{3} \)