Question

if the length of the sides of a triangle are in proportion 25 is to 17 is to 12 and its perimeter is 540 metre then find the length of the largest and smallest altitudes

Answer 1

if the sides are 25x , 17x , 12x where x is any positive no. then

25x + 17x + 12x = 540
54x = 540

x = 10

then the sides are 250m , 170m & 120m.
the semi - perimeter is S = 540/2 = 270 m

now the area of the triangle is
= √ S*(S - 250)*(S - 170)*(S - 120) sq. m

= √ 270*(270 - 250)*(270 - 170)*(270 - 120) sq. m

= √ 270*20*100*150 sq. m

= √ 81000000 sq.m

= 9000 sq.m