the altitude of a triangle is 1 cm less than its base, if the area is 105 cm2. what are the lengths of the base and the altitude

Answer 1

base --- x
height = x-1

area of triangle = (1/2) base x height

(1/2)(x)(x+1) = 105
x^2 + x = 210
x^2 + x - 210 = 0
(x+15)(x-14) = 0
x = -15 or x = 14, but x > 0

base is 14 cm, height is 15 cm

check:
area = (1/2)(15)(14) = 105
all is good!