# The perimeter of a triangle is 60 cm. and the lengths of the sides are in the ratio of 4:5:6. How do you find the length of each side?

Apr 30, 2015

If we name the three sides as $a , b , c$, than the proportion says:

$a : 4 = b : 5 = c : 6$.

Using the property of the proportions (that is using before the compound and than the invertion of terms):

$a : b = c : \mathrm{dr} A r r \left(a + c\right) : \left(b + d\right) = a : b$ $\left(\mathmr{and} c : d\right)$,

than:

$\left(a + b + c\right) : \left(4 + 5 + 6\right) = a : 4 \Rightarrow$

$60 : 15 = a : 4 \Rightarrow a = \frac{60 \cdot 4}{15} = 16$

or:

$60 : 15 = b : 5 \Rightarrow b = \frac{60 \cdot 5}{15} = 20$

or:

$60 : 15 = c : 6 \Rightarrow c = \frac{60 \cdot 6}{15} = 24$.