Question

The triangle has 17cm,12cm and 25cm sides respectively the area is 9000cm.find the largest and smallest altitude of triangle

Answer 1

We know that the area of a triangle is $\frac{1}{2}$* base*height
Case 1:
When base = 17cm
Area = $\frac{1}{2}$*17*h
9000 = $\frac{1}{2}$*17*h
h = $\frac{9000}{17}$
h = 529.411 cm

Case 2:
When base = 12cm
Area = $\frac{1}{2}$*12*h
9000 = $\frac{1}{2}$*12*h
h = $\frac{9000}{12}$
h = 750cm

Case 3:
When base = 25cm
Area = $\frac{1}{2}$*25*h
9000 = $\frac{1}{2}$*25*h
h = $\frac{9000}{25}$
h = 360cm

From this it is seen that the altitude to the base 25cm is the smallest.

This can also be found without calculation as we know that
Area = half*base*height
⇒Base is directly proportional to $\frac{1}{height}$

So the larger the base the smaller the altitude.