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
  • 2
    $\begingroup$ If the sides are in $13:14:15$ and the perimeter is $84$ m, what are the lengths of sides? $\endgroup$ – peterwhy Nov 24 '13 at 9:18
  • $\begingroup$ i had provided all whats given in question. $\endgroup$ – ShujatAli Nov 24 '13 at 9:19
  • $\begingroup$ 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? $\endgroup$ – peterwhy Nov 24 '13 at 9:22
  • $\begingroup$ i had mentioned the exact question now. $\endgroup$ – ShujatAli Nov 24 '13 at 9:23
  • 1
    $\begingroup$ it is given that sides ratio is $13:14:15$ which is quite different from considering that sides are of that length $\endgroup$ – 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)


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