Question

The perimeter of a triangle field is 144m and the ratio of the sides is 3:4:5. The area of the field is

• A. 864 $m^2$
• B. 468 $m^2$
• C. 824 $m^2$
• D. none

Answer 1

The correct option is A 864 $m^2$

Let the sides of triangle are 3x ,4x ,5x

Then perimeter of triangle=3x+4x+5x=12x

But peri meter is 144

$\therefore 12x=144=12$

So length are 36 m ,48m ,60 m

$s=\frac{36+48+60}{2}=72$

then area of triangle= $\sqrt{72(72-36)(72-48)(72-60)}=\sqrt{72\times 36\times 24\times 12}=\sqrt{746469}=864m^2$