Question

The perimeter of two similar triangles are $30cm$ and $20cm$ respectively. If one side of the first triangle is $12cm$, determine the corresponding side of the second triangle.

Answer 1

Let the sides of one triangle be $a,b,c$

Let the sides of another triangle be $A,B,C$

as the triangle are similiar means that

$\frac{a}{A}=\frac{b}{B}=\frac{c}{C}=K$

here $k=constant$

$a=KA$

$b=KB$

$c=KC$

Ratio of perimeters is $\frac{a+b+c}{A+B+C}=\frac{30}{20}$

$\frac{KA+KB+KC}{A+B+C}=\frac{30}{20}=1.5$

$\Rightarrow K=1.5$

According to the question

$12=1.5A$

$A=8$cm