Answer to Question #272890 in Geometry for ghiel

Question

A semi-circle of radius 14 cm is formed from a piece of wire. If it is bent into a rectangle whose length is 1 cm more than its width, find the area of the rectangle.

Answer 1

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 =323cm2