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 =[tex]\frac{2r}{3}[/tex]
The area of the figure = [tex](2r \times \frac{2r}{3}) \times (\frac{\pi r^2}{2})[/tex]
750 = [tex]\frac{(4r^2)}{3} + \frac{\pi r^2}{2}[/tex]
750 = [tex]r^2(\frac{4}{3} +\frac{\pi}{2})[/tex]
750 =[tex]r^2(1.33+1.57)[/tex]
750 = [tex]r^2(2.9)[/tex]
[tex]\frac{750}{2.9} = r^2[/tex]
[tex]258.6 = r^2[/tex]
r = 16.07
Then diameter d = 2(r) = 2(16.07) = 32.14
Now
length of the rectangle = 2r = 32.14 inches
Width =[tex]\frac{2r}{3}[/tex]= [tex]\frac{32.14}{3}[/tex]= 10.71 inches
