the base of a triangle exceeds the height by 9 feet. if the area is 180 square feet,find the length of the base and the height of the triangle

Answer 1

Base ("b") exceeds the height ("h") by 9 feet.

So b = h+9

Since the area of a triangle = (base*height)/2, we can simply substitute h+9 for the base.

So instead of saying (bh)/2 = 180, we rewrite this as

h(h+9)/2 = 180.

Multiplying 2 to b oth sides we get h(h+9) = 360. Now multiply through: h² + 9h = 360, or

h² + 9h - 360 =0.

factoring this out, we get (h+24)(h-15), so our two options for the height are -24 or 15. Since height has to be positive, we know that our height is 15, and our base is 15+ 9, or 24.

Answer:

b=24, h=15