Question

The height of a triangle is 3 feet more than it's base. If the area is 35 ft^2, what is the altitude of the triangle?

Answer 1

h - the height of a triangle
b = h - 3 - the base of a triangle

The formula of athe area of a triangle:


`A_\Delta=(1)/(2)bh`

substitute:


`(1)/(2)(h-3)h=35\ \ \ |\cdot2\\\\(h-3)h=70\\\\h^2-3h=70\ \ \ |-70\\\\h^2-3h-70=0\\\\h^2-10h+7h-70=0\\\\h(h-10)+7(h-10)=0\\\\(h-10)(h+7)=0\iff h-10=0\ \vee\ h+7=0\\\\h=10\ \vee\ h=-7 < 0`

Answer: The altitude of the triangle is equal 10 ft.