Question

In the given figure if the length of chord AB is 7 2 cm, then

the perimeter of the quadrant BPAO is







​

Answer 1

Step-by-step explanation:

fgikeyetiiydanuomou0

Answer 2

The perimeter of quadrant BPAO is (A) 25 cm.

Given:

A quadrant having a chord of length $7\sqrt{2}cm$.

To find:

The perimeter of the quadrant.

Solution:

Step 1

Since, $BPAO$ is a quadrant of a full circle having center O $360^{o}$. Hence quadrant $BPAO$ which is $\frac{1}{4} th$ of a circle will have an angle $90^{o}$ at center 0 or ∠$AOB=90$°. Hence, Δ$AOB$ is a right angles triangle.

Step 2

We also have

$AD=BD$   $;$ since they are the radius of the same quadrants

We have been given a quadrant with a chord $AB=7\sqrt{2}cm$.

Now, in Δ$AOB$, applying Pythagoras theorem, we get

$AB^{2}= BD^{2}+ AD^{2}$

Substituting the given values, we get

$(7\sqrt{2} )^{2} = 2BD^{2}$

$BD^{2}=49$

Hence, $BD=7cm$ , which is the radius of the quadrant.

Step 3

Now,

Perimeter of $BPAO$ will be = $arc(APB)+AD+BD$

Perimeter of $arc(APB)=\frac{1}{4}(2$ π$R)$

Substituting the given values, we get

Perimeter of $APB=\frac{1}{4}2(\frac{22}{7} )(7)=11cm$

Hence,

Perimeter of $BPAO$ will be = $11+7+7$

                                             $=25cm$

Final answer:

Hence, the perimeter of the quadrant $BPAO$ is $(A)$ $25cm.$

Although your question is incomplete, you might be referring to the question below.

In the given figure the length of chord AB is $7\sqrt{2}cm$, then the perimeter of the quadrant $BPAO$ is

$(a) 25cm$      $(b)50cm$    $(c)75cm$    $(d)28cm$