Question 1125927: The lengths of the sides of a triangle are 13cm, 37cm and 40cm. Find the length of the altitude to the longest side, in cm... Found 2 solutions by solver91311, ikleyn:Answer by solver91311(24713) (Show Source):
The standard strategy for solving such problems is to calculate the area of the triangle using the Heron's formula;
then to divide the area by the half of the base.
The perimeter of the triangle is 13 + 37 + 40 = 90 cm; hence, the semi-perimeter is 90/2 = 45 cm.
By the Heron's formula, area of the triangle is
A = = = = = 3*5*16 = 240 cm^2.
Then the length of the altitude to the longest side = = = 12 cm.
