Question

the area of a triangle is 384 square feet. If its base is 8 feet longer than its altitude, find the length of the base and the altitude

Answer 1

A=1/2bh
b=8+h
A=384

384=1/2(bh)
times 2
768=bh
sub
768=b(8+b)
768=8b+b^2
minus 768 both sides
0=b^2+8b-768
factor
0=(b-24)(b+32)
set to zero
b-24=0
b=24

b+32=0
minus 32
b=-32
false, legnths cannot be negative

b=24
24=8+h
minus 8
16=h

base=24ft
altetude=16ft