Chapter 10.5, Problem 17WE

To determine

To construct: a triangle whose perimeter is equal to $CD$ and sides are in the ratio $2:2:3$ .

Explanation of Solution

Given Information:

Draw $\overline{CD}$ about 20 cm long.

Calculation:

Draw $\overline{CD}=20\text{cm}$

Choose any point $Z$ not on $\overline{CD}$ and draw $\overline{CZ}$ .

Take any radius mark off $R$ on $\overline{CZ}$ taking $C$ as center, now take $R$ as center and mark off $S$ on $\overline{CZ}$ again take $S$ as center and mark off $T$ on $\overline{CZ}$ again take $T$ as center mark off $U$ again take $U$ as center and mark off $V$ as center and mark off $W$ and again take $W$ as center and mark off $X$ .

Further $CR=RS=ST=TU=UV=VW=WX$

Draw $\overline{XD}$

At $R,S,T,U,V$ and $W$ draw lines parallel to $\overline{XD}$ intersecting $\overline{CD}$ at $a,b,c,d,e$ and $f$ .

Since $\overline{CD}$ is divided into five equal parts $Ca=ab=bc=cd=de=ef=fd$

After dividing $\overline{CD}$ into seven equal parts taking $b$ as center and $Cb$ as radius draw a circle. And then with same radius but with center $e$ draw a circle again.

Choose anyone of two intersecting point and call it $o$ .

Draw $\overline{ob}$ and $\overline{oe}$ the triangle $oeb$ has perimeter 20cm and side are in ratio $2:2:3$ .