the perimeter of a triangular field is 300cm.and its sides are in the ratio 5:12:13.find the length of the perpendicular from the opposite vertex to the side whose length is 130cm?

Question

the perimeter of a triangular field is 300cm and its sides are
in the ratio 5:12:13 find the length of the perpendicular from the
opposite vertex to the side whose length is 130cm?

nishath.sheik · Answer

Perimeter=300cm
Sides are 5x, 12x, 13x
5x+12x+13x=300
30x=300
x=300/30
x=10
First Side=5x=50
Second Side=12x=120
Third Side=13x=130
s= (50+120+130)/2
=150 (“s” is the semi
perimeter)
According to Heron’s Formula [A=√s(s-a)(s-b)(s-c)],
Area=√ 150(150-50)(150-120)(150-130)
=√150*100*30*20
=3*10*10
=300
Area=1/2 bh
300 =1/2*130*h
300 =65h
h =300/65
h =6 62cm (approx)