the length of the sides of trangle are32cm 42cm and56cm respectively. find the altitude corresponding to the side measuring 56cm.
To find the altitude corresponding to the side measuring 56cm, we first need to determine the area of the triangle using Heron's formula and then apply the area formula using the base and the altitude.
The given lengths of the triangle sides are 32cm, 42cm, and 56cm. Let's denote these sides as a, b, and c.
1. Calculate the semi-perimeter (s) of the triangle using the formula: s = (a + b + c) / 2
In this case, s = (32cm + 42cm + 56cm) / 2 = 65cm
2. Apply Heron's formula to find the area (A) of the triangle:
A = sqrt(s * (s - a) * (s - b) * (s - c))
In this case, A = sqrt(65cm * (65cm - 32cm) * (65cm - 42cm) * (65cm - 56cm))
= sqrt(65cm * 33cm * 23cm * 9cm)
= sqrt(510570cm^2)
≈ 714.92cm^2 (rounded to two decimal places)
3. The area of a triangle can be calculated using the formula: A = (1/2) * base * altitude
Rearranging the formula, we can find the altitude (h) in terms of the area and base:
h = (2 * A) / base
In this case, we know that the side measuring 56cm is the base. Therefore, substituting the values into the formula:
h = (2 * 714.92cm^2) / 56cm
≈ 25.44cm (rounded to two decimal places)
Therefore, the altitude corresponding to the side measuring 56cm is approximately 25.44cm.