Check out the attached image. I've added in points A through D. The points A,B,C are the vertices of the largest triangle. Point D is directly below point A, and point D is on segment BC.Β
To find the area of the largest triangle ABC, we need the base length BC, which is broken up into segments x and y
x = length from C to D y = length from D to B
Let's find x first
Triangle ADC is a right triangle, so we can use the pythagorean theorem a^2 + b^2 = c^2 x^2 + 15^2 = 17^2 x^2 + 225 = 289 x^2 = 289 - 225 x^2 = 64 x = sqrt(64) x = 8
Follow similar steps to find y a^2 + b^2 = c^2 y^2 + 15^2 = 25^2 y^2 + 225 = 625 y^2 = 625 - 225 y^2 = 400 y = sqrt(400) y = 20
Therefore BC = x+y BC = 8+20 BC = 28
The base of the triangle ABC is BC = 28 units b = base b = 28
The height is AD = 15 h = height h = 15
We can now find the area of triangle ABC Area = b*h/2 Area = 28*15/2 Area = 420/2 Area = 210