Question : If the perimeter of a square is $80\;\mathrm{cm}$, then what is the diagonal (in $\mathrm{cm}$) of the square?
Option 1: $20\sqrt{2}$
Option 2: $40\sqrt{2}$
Option 3: $80\sqrt{2}$
Option 4: $20$
Correct Answer: $20\sqrt{2}$
Solution : Let the side length of a square be $ \text{s}\;\mathrm{cm}$. The perimeter of the square $=4 \times \text{s}$ Given that the perimeter is $80\;\mathrm{cm}$. The side length of the square $=\frac{80}{4} = 20\;\mathrm{cm}$ The diagonal of a square $=\sqrt{2} \times \text{s }$ The length of the diagonal of this square $=\sqrt{2} \times 20 = 20\sqrt{2}\;\mathrm{cm}$ Hence, the correct answer is $20\sqrt{2}$.
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Question : If the perimeter of a square is $44\;\mathrm{cm}$, what is the diagonal (in $\mathrm{cm}$) of the square?
Option 1: $11\sqrt{2}$
Option 2: $2\sqrt{11}$
Option 3: $11$
Option 4: $44\sqrt{2}$
Question : In a triangle ABC, if $\angle B=90^{\circ}, \angle C=45^{\circ}$ and AC = 4 cm, then the value of BC is:
Option 1: $\sqrt{2} \mathrm{~cm}$
Option 2: $4 \mathrm{~cm}$
Option 3: $2 \sqrt{2} \mathrm{~cm}$
Option 4: $4 \sqrt{2} \mathrm{~cm}$
Question : If the diagonals of a Rhombus are 12 cm and 16 cm, then what is the perimeter (in cm) of the Rhombus?
Option 1: 20 cm
Option 2: 40 cm
Option 3: 60 cm
Option 4: 80 cm
Question : Find the area of triangle whose sides are 10 cm, 12 cm, and 18 cm.
Option 1: $22 \sqrt{2} \mathrm{~cm}^2$
Option 2: $30 \sqrt{2} \mathrm{~cm}^2$
Option 3: $28 \sqrt{2} \mathrm{~cm}^2$
Option 4: $40 \sqrt{2} \mathrm{~cm}^2$
Question : If two tangents to a circle of radius 3 cm are inclined to each other at an angle of 60°, then the length of each tangent is:
Option 1: $\frac{3 \sqrt{3}}{4} \mathrm{~cm}$
Option 2: $3 \sqrt{3} \mathrm{~cm}$
Option 3: $3 \mathrm{~cm}$
Option 4: $6 \mathrm{~cm}$
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