Question

A rectangle is constructed on a semicircle so that the length equals the diameter. The rectangle is 3 times as long as it is wide. The total area of the figure is 750 in.2. Find the approximate dimensions of the rectangle.

Answer 1

Answer:

Length of the rectangle = 32.14 inches

Width of the rectangle = 10.71 inches

Step-by-step explanation:

Given:

The rectangle is 3 times as long as it is wide

total area of the figure =  750 in.2

To Find:

dimensions of the rectangle = ?

Solution:

The area of the figure = Area of the rectangle + Area of semicircle

Rectangle is 3 times as long as it is wide

Let r be the radius of the semicircle

Then

Length = 2r

Width =$\frac{2r}{3}$

The area of the figure = $(2r \times \frac{2r}{3}) \times (\frac{\pi r^2}{2})$

750  = $\frac{(4r^2)}{3} + \frac{\pi r^2}{2}$

750 = $r^2(\frac{4}{3} +\frac{\pi}{2})$

750   =$r^2(1.33+1.57)$

750 = $r^2(2.9)$

$\frac{750}{2.9} = r^2$

$258.6 = r^2$

r = 16.07

Then diameter d = 2(r)  = 2(16.07) = 32.14

Now

length of the rectangle  =  2r = 32.14 inches

Width =$\frac{2r}{3}$= $\frac{32.14}{3}$= 10.71 inches