Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles. This is a triangle. side a has a length of 12 yards. side b has a length of 20 yards. side c has a length of 28 yards. The altitude to side c has a length of X yards.

Step-by-step answer:

The area of a triangle with given sides 12,20 and 28 yards can be found using Hero's formula:

s = (12+20+28) / 2=30

Area=sqrt (s (s-12) (s-20) (s-28))

=sqrt (30*18*12*2)

=sqrt (36^2*10)

=36sqrt (10)

Using the standard formula for area of triangle

Area = (base) (height) / 2

=28*height/2

=14*height

Since the two methods must produce the same area, we can equate the two values to get

36sqrt (10) = 14*height

which when simplified gives

height

=36sqrt (10) / 14

= 18sqrt (10) / 7

= 8.1 yards (to 1 decimal place)