Question

The perimeter of a square is equal to the perimeter of a rectangle of length $14cm$ and breadth $20cm$ . Find the circumference of a semicircle (approx.) whose diameter is equal to the side of the square.

Answer 1

Hint: In this question use the basic formulas of rectangle, square and circle like $2(l + b),4a,2\pi r,\pi r$. Use this to find the circumference of a semi circle.Considering the side of square be x. Use the formula of perimeter of rectangle and perimeter of square and equate it.We get the value of x i.e side of square and using this find the circumference of the semicircle.

Complete step-by-step answer:
It is given that,
Perimeter of a square is equal to the perimeter of the rectangle.
Hence, we know that the perimeter of a square $ = 4a$ where $a$ is sides.
And perimeter of rectangle $ = 2(l + b)$
As we don’t know the side of a square. Let the side of the square be $X$.
Perimeter of rectangle $ = 2(14 + 20)$
Perimeter of a square $ = 4X$
Hence, According to question : perimeter of a square $ = $perimeter of rectangle ,
$ \Rightarrow 2(14 + 20) = 4X$
$ \Rightarrow X = 17$
Now, we have to find the circumference of a semicircle whose diameter is equal to the side of the square;
Hence, Circumference of a semi circle $ = \pi r$= $\dfrac{{22}}{7} \times \dfrac{{17}}{2}$ where $[2r = X]$
On solving it we get $26.7142857$(approx.)
So, the circumference of a semicircle is $26.7142857$.

Note: It is advisable to remember such basic formulas of perimeter, area and circumference of the rectangle, square , circle and all other shapes as it helps in solving questions and saves time . Eventually it’s difficult to mug up every formula but with practice things get easier , so keep practicing.