Question

The sides of a triangle are in the ratio $3:5:7.$ If the perimeter of the triangle is $60$ cm, then its area

• A. $60\sqrt{3}{\text{cm}}^2$
• B. $30\sqrt{3}{\text{cm}}^2$
• C. $15\sqrt{3}{\text{cm}}^2$
• D. $120{\text{cm}}^2$

Answer 1

The correct option is A $60\sqrt{3}{\text{cm}}^2$

Given sides in the ratio $3:5:7$

perimeter of the triangle $=60cm$

$3x+5x+7x=60$

$\Rightarrow 15x=60$

$\Rightarrow x=60/15$

$\Rightarrow x=4$

$3x=3\times 4=12$cm

$5x=5\times 4=20$cm

$7x=7\times 4=28$cm

Let $S$ be the semiperimeter of given triangle.

$S=\frac{1}{2}(a+b+c)$

$=\frac{1}{2}\cdot 60$

$=30$

Now use formula foe area of triangle

Area $=\sqrt{30(30-12)(30-20)(30-28)}$

$=\sqrt{30\cdot 18\cdot 10\cdot 2}$

$=\sqrt{60\cdot 180}$

$=\sqrt{10800}$

$=\sqrt{3600\cdot 3}$

$=60\sqrt{3}c{m}^2$

$\therefore$ Area of triangle $=60\sqrt{3}c{m}^2$.