# finding the area of triangle

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

• If the sides are in $13:14:15$ and the perimeter is $84$ m, what are the lengths of sides? – peterwhy Nov 24 '13 at 9:18
• i had provided all whats given in question. – ShujatAli Nov 24 '13 at 9:19
• If the sides can be written as $13k$, $14k$ and $15k$ (all in metres) and they add up to $84$ m, what are the lengths of sides? – peterwhy Nov 24 '13 at 9:22
• i had mentioned the exact question now. – ShujatAli Nov 24 '13 at 9:23
• it is given that sides ratio is $13:14:15$ which is quite different from considering that sides are of that length – user87543 Nov 24 '13 at 9:25

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)