1). 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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2). 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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3). 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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4). 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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5). 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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6). The length of a rectangular field is 100 m and its breadth is 40 m. What will be the area of the field?
A). \( \Large (4\times 10^{2}) \)sq m |
B). \( \Large (4\times 10) \)sq m |
C). \( \Large (4\times 10^{4}) \)sq m |
D). \( \Large (4\times 10^{3}) \)sq m |
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7). The area of a rectangular playground is 300 sq m. If the breadth of the field is 15 m, find the length of the field.
A). 20 m |
B). 11 m |
C). 25 m |
D). 10 m |
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8). The ratio of length and breadth of a rectangle is 5 : 3. If length is 8 m more than breadth, find the area of the rectangle.
A). 300 sq m |
B). 250 sq m |
C). 240 sq m |
D). 185 sq m |
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9). The perimeter of a rectangle having area equal to \( \Large \Large 144 cm^{2} \) and sides in the ratio 4 : 9 is
A). 52 cm |
B). 56 cm |
C). 60 cm |
D). 64 cm |
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10). The area of a rectangle lies between \( \Large \Large 40 cm^{2} \) and \( \Large \Large 45 cm^{2} \). If one of the sides is 5 cm, then its diagonal lies between
A). 8 cm and 10 cm |
B). 9 cm and 11 cm |
C). 10 cm and 12 cm |
D). 11cm and 13 cm |
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A) 18 cm

B) 16 cm

C) 14 cm

D) 12 cm

Correct Answer:

Description for Correct answerLet AB = CA = a cm and base = b cm

Now, area of the \( \Large \triangle ABC \)= \( \Large \frac{1}{2}\times b\times h \)

=> 12= \( \Large \frac{1}{2}\times b\times 3 \)

b= \( \Large \frac{12\times 2}{3} \)=8cm

Here, BD=CD=\( \Large \frac{b}{2}=\frac{8}{2} \)=4cm

In right angled \( \Large \triangle ABD \) , by Pythagoras theorem,

AB=\( \Large \sqrt{BD^{2}+AD^{2}} \) => a=\( \Large \sqrt{4^{2}+3^{2}} \)

=\( \Large \sqrt{16+9}=\sqrt{25} \)=5cm

Now, perimeter of an isosceles triangle

= 2a + b = \( \Large 2\times 5+8 \)

= 10 + 8 = 18 cm