SOLUTION: The base of a right triangle is one and half times its height. If its area is 27 sq.m, find its base

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Question 1107361: The base of a right triangle is one and half times its height. If its area is 27 sq.m, find its base
Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
Area (A) of triangle = (1/2) * base * height
:
base is 3x/2, where x is the height of the triangle
:
(1/2) * (3x/2) * x = 27
:
3x^2/4 = 27
:
multiply both sides of = by 4
:
3x^2 = 108
:
x^2 = 36
:
x = 6 or x = -6
:
we reject the negative value
:
base = 3*6/2 = 9 m
:

Answer by ikleyn(52876) About Me  (Show Source):
You can put this solution on YOUR website!
.
Area = %281%2F2%29%2AB%2AH,


B = 1.5H  ====>  27 = %281%2F2%29%2A%281.5%2AH%29%2AH  ====>  54 = 1.5*H^2  ====>  H^2 = 54%2F1.5 = 36  ====>  H = sqrt%2836%29 = 6.


Answer.  Height = 6 meters, Base = 1.5*6 = 9 meters.


Check.   Area = %281%2F2%29%2A9%2A6 = 27 sq. m.    ! Correct !

Solved.