Question

The perimeter of a triangular plot is 750 m. If the sides are in the ratio 5 : 12 : 13, then find the area of the plot.

• A. 18,750 sq. m
• B. 19,550 sq. m
• C. 20,250 sq.m
• D. 21,050 sq.m

Answer 1

The correct option is A 18,750 sq. m

The sides of triangle be 5x, 12x and 13x.
Perimeter of triangular plot = 750
$5x+12x+13x=750$
$30x=750$
$x=25$
$5x=5\times 25=125$
$12x=12\times 25=300$
$13x=13\times 25=325$
$s=750/2=375$
$s-a=375-125=250$
$s-b=375-300=75$
$s-c=375-325=50$
Area of a triangle $=\sqrt{s\times (s-a)\times (s-b)\times (s-c)}$
$=\sqrt{375\times 250\times 75\times 50}$
$=18750$
Area of the plot = 18750 sq. m