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The breadth of a rectangle is 4/5 of the radius of a circle. The radius of the circle is 1/5 of the side of a square, whose area is 625 cm2. What is the area of the rectangle if the length of rectangle is 20 cm?

A150 sqcm

B60 sqcm

C100 sqcm

D80 sqcm

Answer:

D. 80 sqcm

Read Explanation:

Solution:

Given:

The breadth of a rectangle is 4/5 of the radius of a circle

The radius of the circle is 1/5 of the side of a square, whose area is 625 cm2

The length of the rectangle is 20 cm

Formula Used:

The area of the square = a2

The area of the rectangle =l×b

Calculations: 

According to the question, 

The breadth of a rectangle (b) is 4/5 of the radius of a circle (r)

=>b=\frac{4}{5}\times{r}

The radius of the circle (r) is 1/5 of the side of a square (a)


=>r=\frac{1}{5}\times{a}

⇒ The area of square = a2

⇒ 625=a2

⇒ a=25 cm

⇒ The radius of the circle will be =15×a=15×25=5cm=\frac{1}{5}\times{a}=\frac{1}{5}\times{25}=5cm

The breadth of the rectangle will be 

=>b=\frac{4}{5}\times{r}

=>b=\frac{4}{5}\times{5}=4cm

=>The area of rectangle will be =l×b=20×4=80cm2=l\times{b}=20\times{4}=80cm^2


Hence, The area of the rectangle will be​ 80 cm2


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