First error is that the legs are a and b so a should be x and b is 6 and c is 10 the second error is at the end they did not take the square root to get x by itself the real answer should be
X^2 +6^2=10^2
X^2+36=100
X^2 =64
X=8
Point P is the orthocenter of the triangle.
H=-5(t^2 - 16t)
H=-5(t^2 - 16t +64)+320
H=-5(t-8)^2 +320
Vertex is at (8, 320)
The max height is 320 m.
Perimeter = 5.35 * 4 = 21.4 cm
