A triangle with sides 13 cm, 14 cm and 15 cmsmallest altitude in (cm)
Question
A triangle with sides 13 cm, 14 cm and 15 cmsmallest altitude in (cm)
Solution
To find the smallest altitude of a triangle, we first need to find the area of the triangle using Heron's formula.
Heron's formula for the area of a triangle with sides a, b, and c is √[s(s - a)(s - b)(s - c)], where s is the semi-perimeter of the triangle, calculated as (a + b + c) / 2.
In this case, a = 13 cm, b = 14 cm, and c = 15 cm.
So, s = (13 + 14 + 15) / 2 = 21 cm.
Substituting these values into Heron's formula, we get:
Area = √[21(21 - 13)(21 - 14)(21 - 15)] = √[2187*6] = 84 cm².
The altitude of a triangle is given by the formula 2*Area/Base.
Since we want the smallest altitude, we should use the largest side as the base. The largest side in this case is 15 cm.
So, the smallest altitude = 2*84/15 = 11.2 cm.
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