Question

Fill $can/cannot$in the given blank.

We ________ construct $∆XYZ$when $XY=3cm,$$YZ=4cm$and $ZX=5cm$

Answer 1

For constructing a triangle, $thesumoflengthsofanytwosidesofatriangleisgreaterthanthethirdside.$

Step-1: Add sides $XY,YZ$and compare with $ZX$

$$\begin{gathered} XY+YZ \\ 3+4 \\ 7cm \end{gathered}$$

and $ZX=5cm$

So, $XY+YZ>ZX$

Step-2: Add sides $YZ,ZX$and compare with $XY$

$$\begin{gathered} YZ+ZX \\ 4+5 \\ 9cm \end{gathered}$$

and $XY=3cm,$

So, $YZ+ZX>XY$

Step-3: Add sides $ZX,XY$and compare with $YZ$

$$\begin{gathered} ZX+XY \\ 5+3 \\ 8cm \end{gathered}$$

and $YZ=4cm$

So, $ZX+XY>YZ$

Here, $thesumoflengthsofanytwosidesofatriangleisgreaterthanthethirdside.$in all three cases.

We $can$construct $∆XYZ$when $XY=3cm,$$YZ=4cm$and $ZX=5cm$