# The smaller of two similar triangles has a perimeter of 20cm (a+b+c=20cm). The lengths of the longest sides of both triangles are in proportion 2:5. What is the perimeter of the larger triangle? Please explain.

Dec 8, 2015

$\textcolor{w h i t e}{\times} 50$

#### Explanation:

$\textcolor{w h i t e}{\times} a + b + c = 20$

Let sides of larger triangle are $a '$, $b '$, and $c '$. If similarity proportion is $\frac{2}{5}$, then,
$\textcolor{w h i t e}{\times} a ' = \frac{5}{2} a$,
$\textcolor{w h i t e}{\times} b ' = \frac{5}{2} b$,
and$\textcolor{w h i t e}{x} c ' = \frac{5}{2} c$

$\implies a ' + b ' + c ' = \frac{5}{2} \left(a + b + c\right)$
$\implies a ' + b ' + c ' = \frac{5}{2} \textcolor{red}{\cdot 20}$
$\textcolor{w h i t e}{\times \times \times \times \times x} = 50$