Question : The ratio of the length to the width of a rectangle is 3 : 2. If the length of this rectangle is increased by 25% and its width is kept constant, then the area of the rectangle increases by 24 m2. What is the width of this rectangle?
Option 1: 12 m
Option 2: 10 m
Option 3: 8 m
Option 4: 15 m
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Correct Answer: 8 m
Solution : Given, The ratio of the length to the width of a rectangle is 3 : 2. If the length of this rectangle is increased by 25% and its width is kept constant, then the area of the rectangle increases by 24 m2. We know, Area of rectangle = length × width Let the width of the rectangle be $x$. ⇒ The length is $\frac{3x}{2}$ and the area of the rectangle is $\frac{3x^2}{2}$ Now, the length is increased by 25%, So, the new length is $\frac{3x}{2}×(1+\frac{25}{100})=\frac{3x}{2}\times(1.25)=\frac{15x}{8}$ And the area is $\frac{15x^2}{8}$ According to the question, $\frac{15x^2}{8}=\frac{3x^2}{2}+24$ ⇒ $(\frac{15−12}{8})x^2=24$ ⇒ $x^2=\frac{24×8}{3}$ ⇒ $x^2=64$ ⇒ $x=\sqrt{64}$ ⇒ $x=8$ m Hence, the correct answer is 8 m.
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Question : The difference between the length and breadth of a rectangle is 40 metres. If its perimeter is 96 metres, then what will be the area of the rectangle?
Option 1: 254 m2
Option 2: 110 m2
Option 3: 176 m2
Option 4: 152 m2
Question : The length and the breadth of a rectangle are increased by 15% and 10%, respectively. What is the percentage increase in the area of the rectangle?
Option 1: 25%
Option 2: 26.5%
Option 3: 27.5%
Option 4: 26%
Question : The length of each diagonal of a rectangle is 50 cm. If its breadth is 14 cm, then what will be the area of the rectangle?
Option 1: 832 cm2
Option 2: 716 cm2
Option 3: 784 cm2
Option 4: 672 cm2
Question : Each side of a square is 12 cm long. The perimeter of this square is equal to the perimeter of a rectangle whose length is 16 cm. What will be the area of this rectangle?
Option 1: 128 cm2
Option 2: 112 cm2
Option 3: 184 cm2
Option 4: 156 cm2
Question : The breadth of a rectangle is $\frac{4}{5}$th of the radius of a circle. The radius of the circle is $\frac{1}{5}$ of the side of a square, whose area is 625 cm2. What is the area of the rectangle if the length of the rectangle is 20 cm?
Option 1: 150 cm2
Option 2: 600 cm2
Option 3: 100 cm2
Option 4: 80 cm2
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