in a traingle ABC three sides is given 6cm, 5cm and 5.6cm is given, what will be the length of a perpendicular drawn on the side BC with A as vertex
BC (b) times half the length of the perpendicular (h/2) equals the area.
Use Heron's formula for the area in terms of the lengths of the three sides:
http://mste.illinois.edu/dildine/heron/triarea.html
Set that equal to (1/2) b*h and solve for h.
To find the length of the perpendicular drawn from vertex A to side BC, we can use the area of the triangle formula and the length of the base. Here's the step-by-step process:
1. Use the Heron's formula to find the area of the triangle ABC. The formula is given by:
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 = 6cm, b = 5cm, and c = 5.6cm. Calculate the semi-perimeter, s, using the formula above.
2. Substitute the values of a, b, c, and s into the area formula and calculate the area of the triangle ABC.
3. Once you have the area of the triangle, you can use it to find the height (perpendicular) from vertex A to side BC. The formula to find the height is:
Area = 0.5 * base * height
Rearrange the formula to solve for height (h):
height = (2 * Area) / base
In this case, the base is the side BC.
4. Substitute the calculated area from step 2 and the length of the base into the height formula to find the length of the perpendicular from vertex A to side BC.