Answer

Verified

426.6k+ views

**Hint:**We will be using the concept of mensuration to solve the problem. We will use a formula for finding the perimeter of the circle to find the length of the quadrant and then we will find the length of the diagonal of the rectangle to find the required perimeter.

**Complete step by step answer:**

Now, we have to find the perimeter of shaded region given as

Now, we know that the length of arc $\overset\frown{BA}\ is\ \dfrac{1}{4}\left( 2\times \pi \times 10 \right)$

$=5\pi cm.............\left( 1 \right)$

Now, for the perimeter of the shaded region we have to find the sum of length of $BR+RP+PA+\overset\frown{AB}$.

Now, we know that the length of both diagonals of the rectangle is the same.

So, we have OQ = RP. Now, $OQ$ is the radius of the circle. Therefore,

$RP=10cm.........\left( 2 \right)$

Now, we have the perimeter of rectangle that is

\[RO+OP+PQ+RQ=26cm\]

We know that opposite sides of a rectangle are the same. Therefore,

$\begin{align}

& 2\left( RO+OP \right)=26 \\

& RO+OP=13cm \\

\end{align}$

Now, we can see from the figure that,

$\begin{align}

& BR+PA=\left( BO-RO \right)+\left( OA-OP \right) \\

& =BO+OA-\left( RO+OP \right) \\

\end{align}$

Now, BO = OA is the radius of a circle which is equal to 10cm.

Therefore,

$\begin{align}

& BR+PA=20-\left( 13 \right) \\

& =7cm \\

\end{align}$

Now, the perimeter of the shaded region is $BR+RP+PA+arc\overset\frown{BA}$.

Now, from (1), (2) and (3) we have,

$\begin{align}

& =5\pi +10+7 \\

& =\left( 17+5\pi \right)cm \\

\end{align}$

**So, the correct answer is “Option B”.**

**Note:**To solve these types of questions it is important to note the way we have found the length of individual parts and sum them up to find the perimeter of the shaded region also it is very important to note the way we have used the perimeter of the rectangle given to us to find the value of RO+OP.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Which are the Top 10 Largest Countries of the World?

One cusec is equal to how many liters class 8 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

The mountain range which stretches from Gujarat in class 10 social science CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths