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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 = (13+14+15)/2 = 21

 Area = SquareRoot(21(21-13)*(21-14)*(21-15))

Area = 84             not correct dont know where i am wrong
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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 –  Praphulla Koushik Nov 24 '13 at 9:25

1 Answer 1

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)

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