| Direction: In the following questions two quantities I and II are given. Solve both the quantities and choose the correct option accordingly. |
| I. A square and an equilateral triangle have same perimeter. The diagonal of the square is \[12\sqrt{2}\] cm. What is the area of the triangle? |
| II. The length of a rectangle is \[\frac{5}{7}\] of the side of a square. The radius of a circle is equal to the side of the square. The circumference of the circle is 132 cm and the breadth of the rectangle is 8 cm. What is area of the rectangle? |
A) Quantity I > Quantity II
B) Quantity II > Quantity I
C) Quantity I > Quantity II
D) Quantity I < Quantity II
E) Quantity I = Quantity II or relation can't be established.
Correct Answer: B
Solution :
Quantity I. If side of square is x then \[2{{x}^{2}}={{\left( 12\sqrt{2} \right)}^{2}}\] \[\therefore \] x = 12 cm Perimeter of the triangle = 48 cm \[\therefore \] Side \[=\frac{48}{3}=16\,cm\] Area of the equilateral triangle \[=\frac{\sqrt{3}}{4}\times 16\times 16\] \[=64\sqrt{3}\,c{{m}^{3}}\] Quantity II. \[2\pi R=132\] \[\therefore \]\[R=\frac{132\times 7}{2\times 22}=21\,cm\] Side of the square = 21 cm \[\therefore \] Length of the rectangle \[=\frac{5}{7}\times 21\]= 15 cm \[\therefore \] Area\[=15\times 8=120\,c{{m}^{2}}\] \[\therefore \] Quantity I < Quantity II
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