the area of a triangle is 30 ft^2.

Question

the area of a triangle is 30 ft^2.  find the base and altitude if the latter exceeds the former by 7ft^2

Answer 1

height = base + 7

Area = (1/2)(base)(height)

30 = (1/2)(base)(base + 7)

60 = base^2 + 7*base

0 = base^2 + 7 * base - 60

0 = ( base + 12)( base - 5)

base + 12 = 0 ---> base = -12 , is disqualified because it results in negative measures

base - 5 = 0 ---> base = 5

height = base + 7 = 5 + 7 = 12

triangle has height 12 and base 5, which then has area = (1/2)(12)(5) = 30