its an 8th standard question . but i m unable to solve it. please help
Question " the perimeter of a triangle is 84m . the sides are in the ration 13:14:15 . find the area . "
(answer should come this === area = 336 square meter)
what i had tried is this.
$$s = \frac{13+14+15}2 = 21$$
$$Area = \sqrt{(21(21-13)\times(21-14)\times(21-15))}$$
Area = 84 not correct dont know where i am wrong
Best Answer
Since the ratio of sides are in $13:14:15$, let the three sides be $13k$, $14k$ and $15k$ in ascending order.
Now the 3 sides add up to a perimeter length of $84$ m, so
$$\begin{align*} 13k + 14k + 15k =& 84 \text{ m}\\ k =& 2 \text{ m} \end{align*}$$
And so the three sides are $26$ m, $28$ m and $30$ m respectively. Now use Heron's formula to find the area.
(Hint: you should confirm that $s$ is half of perimeter)