Question

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

• A. $900c{m}^2$
• B. $9000c{m}^2$
• C. $1900c{m}^2$
• D. $190c{m}^2$

Answer 1

The correct option is B $9000c{m}^2$

Let sides are 12x, 17x, 25x
$\therefore$ 12x + 17x + 25x = 540
54x = 540
$x=\frac{540}{54}=10$
$\therefore$ Sides are 120 cm, 170 cm, 250 cm
$s=\frac{120+170+250}{2}=270$
Area $=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{270(270-120)(270-170)(270-250)}$
$=\sqrt{270\left(150\right)\left(100\right)\left(20\right)}$
$=10\sqrt{270\times 150\times 20}$
$=10\sqrt{810000}$
$=10\times 900=9000c{m}^2$