Question : The area of a square is 100 sq. cm. Find the length (in cm) of its diagonal.
Option 1: $10\sqrt{2}$
Option 2: $10$
Option 3: $20\sqrt{2}$
Option 4: $20$
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Correct Answer: $10\sqrt{2}$
Solution : The area of a square is given by the formula $A = s^2$, where $s$ is the length of a side. Given that the area is 100 sq. cm. $s = \sqrt{A} = \sqrt{100} = 10 \text{ cm}$ The length of the diagonal $d$ of a square, $d = s\sqrt{2}$ On substituting $s$ = 10 cm, $d = 10\sqrt{2} \text{ cm}$ Hence, the correct answer is $10\sqrt{2}$.
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Question : The sides of a rhombus are 10 cm each and the diagonal measures 16 cm. The area of the rhombus is:
Option 1: 96 sq. cm
Option 2: 160 sq. cm
Option 3: 100 sq. cm
Option 4: 40 sq. cm
Question : The three sides of a triangle are 7 cm, 9 cm, and 8 cm. What is the area of the triangle?
Option 1: $12 \sqrt{3} \;\mathrm{Sq} . \mathrm{cm}$
Option 2: $10\sqrt{3} \;\mathrm{Sq} . \mathrm{cm}$
Option 3: $12 \sqrt{5} \;\mathrm{Sq} . \mathrm{cm}$
Option 4: $2 \sqrt{5} \;\mathrm{Sq} . \mathrm{cm}$
Question : The area of 4 walls of a cuboid is 400 sq. cm. Its length is 15 cm and its height is 8 cm. What is its breadth (in cm)?
Option 1: 12
Option 2: 20
Option 3: 24
Option 4: 10
Question : The length of the diagonals of a rhombus is 40 cm and 60 cm. What is the length of the side of the rhombus?
Option 1: $50 \sqrt{3} \ \text{cm}$
Option 2: $20 \sqrt{3}\ \text{cm}$
Option 3: $10 \sqrt{13}\ \text{cm}$
Option 4: $40 \sqrt{13}\ \text{cm}$
Question : The area and the length of one of the diagonals of a rhombus are 84 cm2 and 7 cm respectively. Find the length of its other diagonal (in cm).
Option 2: 24
Option 3: 48
Option 4: 36
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