Question : The sides of a rectangle are in the ratio of 3 : 8 and its area is 1944 cm2. What is its perimeter?
Option 1: 189 cm
Option 2: 208 cm
Option 3: 198 cm
Option 4: 308 cm
Correct Answer: 198 cm
Solution : Given: Area = 1944 cm2 Side ratio = 3 : 8 Let, Length = $3x$ Breadth = $8x$ Now, $\Rightarrow 3x\ \times 8x\ =\ 1944$ $\Rightarrow 24x^2\ =\ 1944$ $\Rightarrow x^2\ =\ 81$ $\Rightarrow x\ =\ 9$ So, Length $=3\times 9\ =\ 27$ cm Breadth $=8\times 9\ =\ 72$ cm Perimeter of rectangle = 2(length + breadth) $=\ 2(27\ +\ 72)=\ 198$ cm2 Hence, the correct answer is 198 cm2.
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Question : The perimeter of a rectangle is equal to the perimeter of a square. If the length and the breadth of the rectangle are 10 cm and 8 cm, respectively, then what will be the area of the square?
Option 1: 72 cm2
Option 2: 98 cm2
Option 3: 81 cm2
Option 4: 64 cm2
Question : The sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 90 cm. Find its area (in cm2).
Option 1: 150
Option 2: 270
Option 3: 30
Option 4: 60
Question : What is the area of a triangle having a perimeter of 32 cm, one side of 11 cm, and the difference between the other two sides is 5 cm?
Option 1: $8\sqrt{30}$ cm2
Option 2: $5\sqrt{35}$ cm2
Option 3: $6\sqrt{30}$ cm2
Option 4: $8\sqrt{2}$ cm2
Question : Find the area of a rhombus if the perimeter of the rhombus is 52 cm, and one of its diagonals is 10 cm long.
Option 1: 120 cm2
Option 2: 164 cm2
Option 3: 160 cm2
Option 4: 144 cm2
Question : The total surface area of a right circular cylinder is 1848 cm2. The ratio of its total surface area to the curved surface area is 3 : 1. The volume of the cylinder is: (Take $\pi=\frac{22}{7}$)
Option 1: 4312 cm3
Option 2: 3696 cm3
Option 3: 4002 cm3
Option 4: 4851 cm3
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