1). The area of a right angled triangle is 40 sq cm. If its base is equal to 28 cm. find its height
A). \( \Large 3\frac{6}{7} \)cm |
B). \( \Large 4\frac{6}{7} \)cm |
C). \( \Large 2\frac{6}{7} \)cm |
D). \( \Large 5\frac{6}{7} \)cm |
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2). The three sides of a triangle are 15, 25 and x units. Which one of the following is correct?
A). \( \Large 10 < x < 40 \) |
B). \( \Large 10 \le x \le 40 \) |
C). \( \Large 10 \le x < 40 \) |
D). \( \Large 10 < x \le 40 \) |
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3). A triangle with three equal sides has its area equal to \( \Large \Large 3\sqrt{3} \)sq cm. Find its perimeter.
A). \( \Large 6\sqrt{3} \)cm |
B). \( \Large 2\sqrt{3} \)cm |
C). \( \Large 5\sqrt{3} \)cm |
D). \( \Large 7\sqrt{3} \)cm |
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4). 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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5). 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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6). 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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7). 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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8). 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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9). 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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10). 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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A) \( \Large 8\sqrt{63} \)sq cm

B) \( \Large 5\sqrt{63} \)sq cm

C) \( \Large 6\sqrt{53} \)sq cm

D) \( \Large 7\sqrt{93} \)sq cm

Correct Answer:

Description for Correct answerGiven that,

a=8cm, b = 10 cm and c=12cm

We know, that

s = \( \Large \frac{a+b+c}{2} \) = \( \Large \frac{8+10+12}{2} \)

= \( \Large \frac{30}{2} \)=15cm

(s-a)=(15-8)=7cm

(s-b)=(15-10)=5cm

(s-c)=(15-12)=3cm

Area = \( \Large \sqrt{s(s-a)(s-b)(s-c)} \)

= \( \Large \sqrt{15\times 7\times 5\times 3} \)= \( \Large \sqrt{1575} \)= \( \Large \sqrt{25\times 63} \)

= \( \Large 5\sqrt{63} \)sq cm.