Question

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

Answer 1

Step-by-step explanation:

let the ratio be 12x, 17x ,25x

12x +17x +25x =540

54x =540

x = 540 ➗ 54

x = 10

12x = 12 x 10 = 120

17x = 17 x 10= 170

25x = 25 x 10=250

Sides of the triangle will be 120 cm, 170 cm, and 250 cm.

using herons formula ( see the picture)

plz mark brainliest if useful

Answer 2

$\huge\sf\red{SIDES:-}$

$\implies$$\large\sf{12x}$

$\implies$$\large\sf{17x}$

$\implies$$\large\sf25x{}$

━━━━━━━━━━━━━━━

$\huge\sf\purple{PERIMETER:-}$

$\implies$$\large\sf{12x+17x+25x}$

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

$\implies$$\large\sf{540=54x}$

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

$\implies$$\large\sf{x=10}$

━━━━━━━━━━━━━━━

$\huge\sf\green{THEN,}$

$\implies$$\large\sf{a=120}$

$\implies$$\large\sf{b=170}$

$\implies$$\large\sf{c=250}$

━━━━━━━━━━━━━━━

$\huge\sf\orange{By\:Heron's\:Formula:-}$

$\implies$$\large\sf{√s(s-a)(s-b)(s-c)}$

$\implies$$\small\sf{√270(270-120)(270-270)(270-250)}$

$\implies$$\small\sf{√27×10×15×10×10×10×2×10}$

$\implies$$\small\sf{10×10√3×3×3×3×5×2×2×5}$

$\implies$$\large\sf{100×3×3×5×2}$

$\implies$$\large\sf\blue{{9000cm}^{2}}$