Question

In this figure, AOB is a quarter circle of radius 10 cm and PQRO is a rectangle of perimeter 28 cm. The perimeter of the shaded region is a + b*pie. Find a - 2b = ?

Answer 1

Answer:

Value of (a - 2b) is 6.

Step-by-step explanation:

Since radius of a circle is 10 cm. Therefore, the circumference of the circle = 2πr

Circumference of the quarter circle (Arc AB)= $\frac{2\pi r}{4}$

= $\frac{20\pi }{4}$

= 5π cm

Perimeter of rectangle PQRS = 28 cm

2(OR + OP) = 28

OR + OP = 14

Now PA + RB = (OB + OA) - (OR + OP)

                      = (10 + 10) - (14)

                      = 20 - 14

                      = 6 cm

Since PR = OQ [Diagonals of a rectangle are same in length]

OQ = 10 cm [Radius of the rectangle]

Therefore, PR = 10 cm

Since perimeter of the shaded area = Arc AB + RB + RP + PA                                                                   = Arc AB + RP + (RB + PA)

                                                            = 5π + 10 + 6

                                                            = 16 + 5π

If we compare this perimeter with (a + bπ) then,

a = 16, b = 5

Now we have to  find the value of (a - 2b).

a - 2b = 16 - 2×5

         = 16 - 10

         = 6

Therefore, value of (a - 2b) = 6

Learn more about the perimeter of a quarter circle from https://brainly.in/question/8980417

Answer 2

Answer:

you can answer this question by following image by rajput harshit