SOLUTION: A certain triangle has area 6 cm^2. If you know that its base is one less than it height, what are the base and height of the triangle?

Algebra ->  Triangles -> SOLUTION: A certain triangle has area 6 cm^2. If you know that its base is one less than it height, what are the base and height of the triangle?      Log On


   

Question 212421: A certain triangle has area 6 cm^2. If you know that its base is one less than it height, what are the base and height of the triangle?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
AreaOfTriangle+=+%28Base+%2A+Height%29%2F2
Let the height be represented by h.
You are told the base, b, is h-1
AreaOfTriangle+=+%28Base+%2A+Height%29%2F2
AreaOfTriangle+=+%28b+%2A+h%29%2F2
AreaOfTriangle+=+%28%28h-1%29%2A+h%29%2F2
6+=+%28%28h-1%29%2A+h%29%2F2
12+=+%28h-1%29%2A+h+
12+=+h%5E2+-h
0+=+h%5E2+-h+-+12
0+=+%28h-4%29%28h%2B3%29
So h is either 4 or -3
Since the height can't be negative, it must be 4
Which makes the base 4-1+=+3
Check your answer, is the area of a triangle with a base of 3 and a height of 4 equal to 6???