Question

the side of a triangle are in the ratio 13: 14:15:and its perimeter is 84cm find the area if the triangle

Answer 1

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

$\textbf{\underline{PQR\;be\;the\;sides\;of\;Triangle}}$

$\textbf{\underline{First\;Side}}$

P = 13p

$\textbf{\underline{Second\;Side}}$

Q = 14p

$\textbf{\underline{Third\;Side}}$

R = 15p

Now,

Perimeter of ∆ = P + Q + R

$\textbf{\underline{Substitute\;the\;values}}$

84 = 13p + 14p + 15p

84 = 27p + 15p

84 = 42p

$\tt{\rightarrow\dfrac{84}{42}=p}$

p = 2

Hence,

Now

$\tt{\rightarrow S=\dfrac{Perimeter}{2}}$

$\tt{\rightarrow\dfrac{84}{2}}$

= 42

${\boxed{\sf\:{Using\;Heron\;Formula}}}$

$\tt{\rightarrow\sqrt{s(s-a)(s-b)(s-c)}}$

$\tt{\rightarrow\sqrt{43(42-26)(42-28)(42-30)}}$

$\tt{\rightarrow\sqrt{42\times 16\times 14\times 12}}$

$\tt{\rightarrow\sqrt{42\times 224\times 12}}$

$\tt{\rightarrow\sqrt{42\times 2688}}$

$\tt{\rightarrow\sqrt{112869}}$

= 336