Question

Sides of a triangle are in the ratio 12:17:25 and its perimeter is 540cm. find its area.

Answer 1

perimeter of triangle =

$540 \div 3 = 180$

Let 12 be a, 17 be b, 25 be c

According to Heron's Formula,

semi-perimeter =

$a + b + c \div 2 \\ \\ 12 + 17 + 25 = 54 \\ 54 \div 2 = 27$

Area of triangle =

$\sqrt{27 \times 15 \times 10 \times 2 }$

By Splitting Method

$\sqrt{3 \times 9 \times 2 \times 5 \times 2 \times 1}$

$3 \times 9 \times 2 \times 5 = 270sq \: cm$

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Answer 2

$\huge\tt{\underline{\underline{Solution :-}}}$

Let one side of triangle= 12x

Let 2nd side of triangle= 17x

Let 3rd side of triangle= 25x

$\textsf{12x+17x+25x=540\:cm}$

$\textsf{54x=540cm}$

$\huge\sf\frac{540}{54}$

$\textsf{x=10cm}$

★a=12x=12×10=120cm

★b=17x=17×10=170cm

★c=25x=25×10=250cm

____________________________

s=$\huge\sf\frac{a+b+c}{2}$= $\huge\sf\frac{540}{2}$ = 270cm.

______________________________

Area of triangle by using heron's formula:-

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

$\sf\sqrt{270(270-170)(270-170)(270-250)}$

$\sf\sqrt{270(150)(150)(20)}$

$\sf\sqrt{81000000}$

9000$\sf{cm}^{2}$