Question

Side of a traingle in ratio 12:17:25 and its permeter is 540 cm .Find its area .

Answer 1

$\huge{\bf{\underline{\red{Solution :}}}}$

Suppose the sides of a triangle 12x , 17x and 25x (in meter)

Perimeter of Triangle = Sum of three sides

⇒540 = 12x + 17x + 25x

⇒540 = 54x

x = $\bold{\sf{\frac{540}{54}}}$

x = 10

Therefore ,

The sides of triangle are :

• a = 25x = 25 x 10 = 250 m
• b = 17x = 17 x 10 = 170 m
• c = 12x = 12 x 10 = 120 m

So , Semi- Perimeter :

$\implies \bold{\sf{\frac{a + b + c}{2}}}$

$\implies \bold{\sf{\frac{250 + 170 + 120}{2}}}$

$\implies \bold{\sf{\frac{540}{2} = 270 \ m }}}$

Now Using Heron's Formula to Find Area of Triangle :

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

$\implies \bold{\sf{\sqrt{270(270 - 250)(270-170)(270 -120)}}}$

$\implies \bold{\sf{\sqrt{270 \times 20 \times 100 \times 150}}}$

$\implies \bold{\sf{2 \times 2 \times 3 \times 3 \times 5 \times 5 \times 10}}}$

$\implies \bold{\sf{\boxed{9000 \ m^{2}}}}$

Area of triangle is 9000 m²(Answer)

$\rule{200}2$

Answer 2

$\large \underline{ \blue{ \boxed{ \bf \green{Required \: Answer}}}}$

Answer in Attatched File...