SOLUTION: Write a quadratic equation and solve. The altitude of a triangle is 3cm less than its base. The area of the triangle is 90cm^2. Find the base and altitude.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Write a quadratic equation and solve. The altitude of a triangle is 3cm less than its base. The area of the triangle is 90cm^2. Find the base and altitude.      Log On


   

Question 971394: Write a quadratic equation and solve. The altitude of a triangle is 3cm less than its base. The area of the triangle is 90cm^2. Find the base and altitude.
Found 2 solutions by macston, josgarithmetic:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
B=base; H=height (altitude)=B-3cm; A=area=90cm^2
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%281%2F2%29BH=A Substitute for H.
%281%2F2%29B%28B-3cm%29=90cm%5E2 Multiply each side by 2.
B%5E2-3B=180cm%5E2 Subtract 180cm^2 from each side.
B%5E2-3B-180=0
%28B-15%29%28B%2B12%29=0
B-15=0 or B%2B12=0
B=15 or B=-12
ANSWER 1: The base is 15 centimeters.
H=B-3cm
H=15cm-3cm
H=12+cm
ANSWER 2: The height (altitude) is 12 centimeters.








Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
a, altitude
b, base
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system%28a=b-3%2C+%281%2F2%29b%2Aa=90%29

ba=180
b%28b-3%29=180
b%5E2-3b-180=0

Going directly to general solution of quadratic equation:
b=%283%2B-+sqrt%289%2B4%2A180%29%29%2F2
b=%28-3%2B-+27%29%2F2
b=24%2F2, from the PLUS form
highlight%28b=12%29
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highlight%28a=9%29