Question

$△LMN\sim$ $△XYZ$. In $△LMN,LM=6cm,MN=6.8cm,LN=7.6cm$ and $\frac{LM}{XY}=\frac{4}{5}$; Construct $△XYZ$.

Answer 1

The sides of $△XYZ$ will be $\frac{5}{4}$ times the sides of $△LMN$

$\therefore XY=\frac{5}{4}\times LM=\frac{5}{4}\times 6=7.5cm$

$YZ=\frac{5}{4}\times MN=\frac{5}{4}\times 6.8=8.5cm$

$XZ=\frac{5}{4}\times LN=\frac{5}{4}\times 7.6=9.5cm$

Construction:

Step $1$: Draw base $XZ=9.5cm$ with a ruler.

Step $2$: Place the compass on point $X$ and measure an arc with length of the compass as $XY=7.5cm$.

Step $3$: Place the compass on point $Z$ and measure an arc with length of the compass as $YZ=8.5cm$.

Step $4$: Mark the intersection point of the arcs in steps $2$ and $3$ as point $Y$ and draw lines joining $X-Y$ and $Z-Y$.

$△XYZ$ is the required triangle.