Question

The sides of a triangle are in
the ratio 12:17:25 and its
perimeter is 540 cm. the area
is
(a) 1000 cm2
(b) 5000 cm2
(c) 9000 cm2
(d) 8000 cm2​

Answer 1

$\huge \fbox{\green{Answer:-}}$

$\large \bf{\red{Given:-}}$

$\sf \rightarrow{Sides \: of \: triangle(in\:ratio) \: is \: 12:17:25.}$

$\sf \rightarrow{Perimeter \: of \: triangle \: is \: 540cm.}$

$\large \bf{\red{To \: find:}}$

$\sf \leadsto{Area \: of \: triangle.}$

$\large \bf{ \red{Formula \: used:}}$

$\boxed{\bf{Perimeter \: of \: triangle=sum \: of \: all \: sides}}$

$\boxed {\bf{Area \: of \: triangle= \sqrt{s(s - a)(s - b)(s - c)} }}$

$\sf{Where,s=semi-perimeter \: of \: triangle}$

$\sf{a,b \: and \: c \: is \: the \: sides \: of \: the \: triangle.}$

$\bf \red{According \: to \: Question:}$

${\sf{⇒Perimeter \: of \: triangle=sum \: of \: all \: sides}}$

$\implies \sf{540cm = 12x + 17x+ 25x}$

$\implies \sf{540cm = 54x} \\ \implies \sf{ \frac{540cm}{54} = x}$

$\sf \implies{x = 10}$

$\sf \implies{s = \frac{540}{2} = 270cm}$

$\sf{a = 12x = 12 \times 10 = 120}$

$\sf{b = 17x = 17 \times 10 = 170}$

$\sf{c = 25x = 25 \times 10 = 250}$

$\sf \implies{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c))} }$

$\sf \implies{Area \: of \: triangle = \sqrt{270(270- 120)(270 - 170)(270 - 250)} }$

$\sf \implies{Area \: of \: triangle = \sqrt{270 \times 150 \times 100 \times 20} }$

$\sf \implies{Area \: of \: triangle = \sqrt{8,10,00,000}}$

${ \sf \implies{Area \: of \: triangle = 9,000cm²}}$

$\fbox{\sf {{Area \: of \: triangle = 9,000cm²}}}$

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