SOLUTION: the base of a triangle is four more than twice its height. if the area of the triangle is 42 square centimeters, find its base and height

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Question 324048: the base of a triangle is four more than twice its height. if the area of the triangle is 42 square centimeters, find its base and height
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For a triangle,
A=%281%2F2%29bh
A=%281%2F2%29%284%2B2h%29h=42
h%282h%2B4%29=84
2h%5E2%2B4h-84=0
h%5E2%2B2h-42=0
Use the quadratic formula,
h+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-42%29+%29%29%2F%282%2A1%29+
h+=+%28-2+%2B-+sqrt%28+4%2B168+%29%29%2F2+
h+=+%28-2+%2B-+sqrt%28+172%29%29%2F2+
h+=+%28-2+%2B-+2sqrt%28+43+%29%29%2F2+
h+=+-1+%2B-+sqrt%28+43+%29+
Only the positive result makes sense in this problem.
highlight%28h=-1%2Bsqrt%2843%29%29
Then,
b=-2%2B2sqrt%2843%29%2B4
highlight%28b=2%2B2sqrt%2843%29%29