To find the altitude of the triangle, we need to use the formula for the area of both shapes. The area of a parallelogram is calculated using the formula:
Area of Parallelogram = Base × Height
Given that the height (altitude) of the parallelogram is 100m, we can write:
Area of Parallelogram = Base × 100
Now, for the triangle, the formula for the area is:
Area of Triangle = (Base × Height) / 2
Since we’re told that the areas of the triangle and the parallelogram are equal, we can set the two area equations equal to each other:
Base × 100 = (Base × Height of Triangle) / 2
We can simplify this equation. First, let’s multiply both sides by 2 to eliminate the fraction:
2 × (Base × 100) = Base × Height of Triangle
This simplifies to:
200 × Base = Base × Height of Triangle
If we divide both sides by Base (assuming Base is not zero), we have:
200 = Height of Triangle
Therefore, the altitude of the triangle is:
Height of Triangle = 200m
In conclusion, if a triangle and a parallelogram have equal areas and the altitude of the parallelogram is 100m, then the altitude of the triangle would be 200m.