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(\\pi+2)" where, r=radius and "\\pi=\\frac{22}{7}"

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

"=(14+28)cm"

"=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"

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

Now in our problem

"2(2x+2)=72"

"2x+2=36"

"x+1=18"

"x=17"

The width of the rectangle is 17cm


The length of the rectangle is "x+2"

"=17+2=19"

therefore the length of the rectangle is 19cm


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

"=17\\times19"

"=323cm^2"


Area of the rectangle is "323cm^2"


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