Question

If the area covered
by the semi-circle in
the given rectangle
is 77 cm?, then the
ratio of the green
region to the purple
region is:.​

Answer 1

Answer:

Here is your answer I hope it will help you.

Answer 2

Given:

• The area of semi circle is $77cm^{2}$.
• The semicircle region is in the rectangular region.

To find:

• The ratio between the green region and the purple region.

Step by step explanation:

• Let the region in the rectangular field is Green.
• Let the region in the semicircular field is Purple.
• We know the area of semicircle is,

        $\frac{1}{2}$π$r^{2}$

• As we know that the area of semicircle is $77cm^{2}$, so

        $\frac{1}{2}$π$r^{2} =77cm^{2}$

• By substituting the value of π as $\frac{22}{7}$, the above equation becomes,

        $(\frac{1}{2})(\frac{22}{7})r^{2} =77cm^{2}$

• By solving the above equation in LHS and taking the terms from LHS other than $r$ from LHS to RHS we get,

        $r^2=(7)(7)$

• Therefore,

        $r=7cm$.

• So the length of the rectangle is twice the radius of the semicircle since semicircle in inside the rectangle.

        $l=2r$

• Therefore,

        $l=(2)(7)\\l=14cm$

• Breadth of the rectangle is equal to the radius of the semicircle so,

        $b=7cm$

• Now the area of the rectangle is ,

        $A=lb$

• By substituting the values of length and breath in the above equation,

        $A=(14)(7)$

• Therefore area of rectangle is,

        $A=98cm^2$

• Now the area of green region that is the region in the rectangluar field is,

       $Area of green region =area of rectangle-area of semicircle$

• Substitute the values in the equation,

       $Area of green region =98-77$

• Therefore,

       $Area of green region=21cm^2$

• Therefore the ratio is $21:77$

Final answer:

• The ratio of the green region and the purple region is $21:77$.