Question

the lengths of the three altitudes of a triangle are 6x,4x and 3x units respectively.if it's perimeter is 18 units then it's area is.

Answer 1

This is the concept of algebra, for us to calculate the area of the triangle we need the value of x. Therefore, we shall obtain this from the perimeter.

P=6x+4x+3x=18
13x=18
x=18/13
x=1.385
The length of the altitudes will be:
6x=6×1.385=8.31 
4x=4×1.385=5.54
3x=3×1.385=4.155
the area will be given by Heron's formual:
Area=√[p(p-a)(p-b)(p-c)]
p=(a+b+2)/2
=(8.31+5.54+4.155)/2
=9.0025
therefore:
A=√[9.00(9-8.31)(9-5.54)(9-4.155)
A=104.64 sq. units