SOLUTION: The base and height of a triangle total 14 cm and the area is 20 cm2. Find the dimensions of the triangle.

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Question 1083215: The base and height of a triangle total 14 cm and the area is 20 cm2. Find the dimensions of the triangle.
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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b + h   = 14,    (1)
%281%2F2%29%2Ab%2Ah = 20.    (2)


Transform:

b  = 14 - h,     (1')
b*h    = 40.     (2')


Substitute (1') into (2')). You will get

(14-h)*h) = 40,

14h - h^2 = 40,

h^2 - 14h + 40 = 0,

Factor left side:

(h-10)*(h-4) = 0.


There are two solutions:

1)  h = 10.   Then b = 4.

2)  h = 4.    Then b = 10.


Answer.  There are two solutions:  1)  h = 10, b = 4   and   2)  h = 4, b = 10.

Solved.