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Mensuration MCQ 3:(Circle, rectangle, square)

Mensuration MCQ 3: The length of a rectangle is two – fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?

a) 140                     b) 156                       c) 175                           d) 214

Solution:

 

We first comes to the second point of the quesrtion i-e ” the radius of the circle is equale to the side of the square whose area is 1225 sq. units”

We know that if (suppose ) side of a square is ‘x’ then its area is

\[ x^2 \]

So for given square if its side is ‘x’, we get;

\[ x^2=1225 \]

or

\[ x=\sqrt 1225=35 \]

So, radius of the circle according to given statement – is ;

\[ Radius=35 units \]

Now we come to the first part of the statement – according to which length of the rectangle is 2/5th of the radius of the circle i-e

\[ RectangleLength=\frac{2}{5}\times radius=\frac{2}{5}\times 35=14 units \]

So the length of the rectangle is 14 units . We have also been given the breadth of the rectangle as 10 units.

But we know;

\[ Rectangle Area =Length\times Breadth=14\times 10=140 squnits \]

So, the option a is correct answer

 

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