Question

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?

• A. 150 sqcm
• B. 60 sqcm
• C. 100 sqcm
• D. 80 sqcm

Answer 1

Answer:

D. 80 sqcm

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 $=\frac{1}{5}\times{a}=\frac{1}{5}\times{25}=5cm$

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 $=l\times{b}=20\times{4}=80cm^2$

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