given the triangle ABC with BC=7cm AD=7cm and AD is the altitude of the triangle find the area of ∆ABC?
recall that for a triangle
area = 1/2 base * height
So, use BC as the base and AD as the height
To find the area of triangle ABC, we can use the formula:
Area = (base * height) / 2
In this case, AD is the altitude (height) of the triangle, and BC is the base. Since we know that AD = 7 cm, we need to find BC.
Triangle ABC is a right-angled triangle, with AD as the altitude. This means that AD forms a right angle with BC. Using the Pythagorean theorem, we can find BC as follows:
BC² = AB² - AC²
We know that AB = BC + AC, so we can substitute BC + AC for AB:
BC² = (BC + AC)² - AC²
Expanding this equation, we get:
BC² = BC² + 2*BC*AC + AC² - AC²
The AC² term cancels out, leaving us with:
0 = 2*BC*AC
Since AC cannot be zero (as that would make the triangle degenerate), we can divide both sides by AC:
0 / AC = 2*BC*AC / AC
0 = 2*BC
Dividing both sides by 2, we find:
0 / 2 = BC
BC = 0
This implies that the base of the triangle is 0, which does not make sense geometrically. Therefore, there is no non-degenerate triangle with the given measures.
Hence, we cannot calculate the area of triangle ABC.