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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Correct Answer: 80 cm2
Solution : The breadth of a rectangle is $\frac{4}{5}$ 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 cm$^2$ The length of the rectangle is = 20 cm Formula Used: The area of the square = $a^2$ The area of the rectangle = $l \times b$ Calculations: According to the question, The breadth of a rectangle (b) is $\frac{4}{5}$ of the radius of a circle (r) ⇒ $b = \frac{4}{5}\times r$ The radius of the circle (r) is $\frac{1}{5}$ of the side of a square (a) ⇒ $r= \frac{1}{5} \times a$ The area of square = $a^2$ $625 = a^2$ ⇒ $a = 25$ cm The radius of the circle will be = $\frac{1}{5}\times a$ = $\frac{1}{5}\times 25$ = 5 cm The breadth of the rectangle will be $b = \frac{4}{5}\times r$ $b = \frac{4}{5}\times 5$ = 4 cm The area of the rectangle will be = $l \times b$ = 20 × 4 = 80 cm$^2$ Hence the correct answer is 80 cm$^2$.
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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 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 : The length of each side of a square is 16 cm. What is the area of the square?
Option 1: 112 cm2
Option 2: 176 cm2
Option 3: 128 cm2
Option 4: 256 cm2
Question : A square of side $p$ is taken. A rectangle is cut out from this square such that the length of one side of the rectangle is equal to half of the length of one side of the square and the length of another side of the rectangle is equal to $\frac{1}{3}$rd of the length of the first side of the rectangle. What is the area of the portion of the square that remained after the rectangle was cut out?
Option 1: $\frac{7}{8} p^2$
Option 2: $\frac{3}{4} p^2$
Option 3: $\frac{11}{12} p^2$
Option 4: $\frac{15}{16} p^2$
Question : 5 times the perimeter of a square is 600 cm. What will be the area of this square?
Option 1: 900 cm2
Option 2: 1150 cm2
Option 3: 750 cm2
Option 4: 480 cm2
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