what is the height of a triangle whose sides are 13 , 20 and 21 cm
Use this formula:
height=2*K/base
The given sides look suspiciously like the sides of a Heronian triangle, one that is comprised of two Pyhagorean triangles with a common altitude. In reality, the triangle is the 5-12-13 triangle joined to the 12-16-20 triangle having the common altitude of 12.
To find the height of a triangle, we can use the formula:
Area = (base * height) / 2
In this case, the base of the triangle is the side of length 20 cm. Let's assume this is the base, and the height is h.
Now, we need to find the area of the triangle. We can use Heron's formula to calculate the area:
Area = √(s * (s - a) * (s - b) * (s - c))
where a, b, and c are the lengths of the triangle's sides, and s is the semi-perimeter (s = (a + b + c) / 2).
In our case, a = 13 cm, b = 20 cm, and c = 21 cm.
First, let's calculate the semi-perimeter:
s = (13 + 20 + 21) / 2 = 54 / 2 = 27
Now, let's calculate the area:
Area = √(27 * (27 - 13) * (27 - 20) * (27 - 21)) = √(27 * 14 * 7 * 6) = √(5292) = 72.68 cm² (approx.)
Now, we have the area and the base length. We can rearrange the formula for the area to find the height:
Height = (2 * Area) / Base = (2 * 72.68) / 20 = 5.82 cm (approx.)
Therefore, the height of the triangle is approximately 5.82 cm.