Question

The sides of a triangle are in the ratio 3 : 4 : 5. If its perimeter is 36 cm, then the area of the triangle is ___.

• A. $57c{m}^2$
• B. $54c{m}^2$
• C. $56.5c{m}^2$
• D. $64c{m}^2$
• E. None of these

Answer 1

The correct option is B $54c{m}^2$

The sides of the triangle are
$a=\frac{3}{12}\times 36=9cm,b=\frac{4}{12}\times 36=12cmc=\frac{5}{12}\times 36=15cms=\frac{a+b+c}{2}=\frac{36}{2}=18cm$
$\therefore$ Area $=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{18(18-9)(18-12)(18-15)}=\sqrt{18\times 9\times 6\times 3}=\sqrt{9^2\times 2^2\times 3^2}=9\times 2\times 3=54c{m}^2.$