The length of the shorter side of the rectangle on which the semicircle is drawn onto one of the longer sides is 10.54 cm.
What is the area of a rectangle?
Area of rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,
[tex]A=a\times b[/tex]
Here, (a)is the length rectangle and (b) is the width of the rectangle
A semicircle is drawn onto one of the longer sides of a rectangle. The longer side of the rectangle measures 10 centimeters.
As the semicircle is drawn onto one of the longer sides. Thus the length of the longer side will be equal to the length of the radius of the semicircle.
Thus, the length of the semicircle is 10 cm. The area of the semicircle is,
[tex]A=\dfrac{\pi r^2}{2}[/tex]
Hear (r) is the radius of the semicircle. Thus the area of the semicircle with 10 cm radius is,
[tex]A_s=\dfrac{3.14 (10)^2}{2}\\A_s=157\rm \; cm^2[/tex]
Suppose the shorter length of the rectangle is x cm long. Thus, the area of the rectangle is,
[tex]A_r=10\times x[/tex]
As, the total area of the figure is 51.4 square centimeters. Thus,
[tex]A_t=A_s+A_r\\51.4=157+10x\\10x=105.4\\x=10.54\rm \;cm[/tex]
Hence, the length of the shorter side of the rectangle on which the semicircle is drawn onto one of the longer sides is 10.54 cm.
Learn more about the area of rectangle here;
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