Answer to Question #191647 in Geometry for Angelo

Question #191647

A semi-circle of radius 14 cm is formed from a piece of wire. If it is bent into a rectangle whose length is 2 cm more than its width, find the area of the rectangle.


1
Expert's answer
2021-05-11T13:59:48-0400

Given that a semi circle of radius 14cm is formed from a piece of wire

Now, the perimeter of the semi circle is r(π+2)r(\pi+2) where, r=radius and π=227\pi=\frac{22}{7}

Now the perimeter =14(227+2)cm=14(\frac{22}{7}+2)cm

=(14+28)cm=(14+28)cm

=72cm=72cm

This is the perimeter of the rectangle

Let the width of the rectangle is x cm

therefore the length is 2cm more than its width

=(x+2)cm=(x+2)cm

Now the perimeter of rectangle is 2[(x+2)+x]cm2[(x+2)+x]cm

Now in our problem

2(2x+2)=722(2x+2)=72

2x+2=362x+2=36

x+1=18x+1=18

x=17x=17

The width of the rectangle is 17cm


The length of the rectangle is x+2x+2

=17+2=19=17+2=19

therefore the length of the rectangle is 19cm


Now, the area of the rectangle is given by L×WL\times W

=17×19=17\times19

=323cm2=323cm^2


Area of the rectangle is 323cm2323cm^2


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