Math Question Help
I'm in Grade 10 math and hopefully you guys find this easy. The question is:
What is the maximum area of a triangle having 15 cm as the sum of its base and height?
I don't really know how to go about this question. You don't have to give me the answer, but an explanation of what to do would be nice.
Doing completion of squares. Quadratics. Factoring. Parabolas. Whatnot.
April 19, 2013
7 Comments • Newest first
b+h = 15
(b*h)/2 = ?
b = 15-h
[(15-h)*h]/2 = a
an then search for the vertex of the parabola
Really easy.
Test it out with 4.
assume it has a base of 2 and a height of 2 making the area 2
the assume it has a base of 3 and a height of 1 resulting in an area of 1.5
based off of this pattern you can tell that you just divide the number in half (15/2) to get the base and height (7.5 and 7.5)
Got it! Thanks for the help everyone!
The way I think about these questions without all of the above math is that you want the 2 values to be as close to the same. 9 + 6 = 15 but 1/2(9)(5) = 22.5. 7.5 + 7.5 also equals 15 but 1/2(7.5)^2 = 28.125 and 7.5 is what above got
56.25/2=28.125
7.5x7.5=56.25/2=28.125
EDIT: Wow did I read that wrong. Brb redoing..
1/2bh=A
b+h=15
From here I'd use optimization, but you're in 10th grade so I'm guessing you haven't learned that yet..:S. Hmm..well you do know that your highest bh should be when both your b and your h are equal..so b=7.5, h=7.5, so just plug in:
1/2(7.5)(7.5)=A to get your max area, which is 28.125.
[url=http://img59.imageshack.us/img59/5959/scan0007bf.jpg]My work.[/url]
So basically you have to set up two equations.
Then you isolate a variable and plug it into the other equation.
You get a quadratic.
You use the vertex formula -b/2a. On a graph, this finds the point in which the parabola is at its highest or lowest.
Simplify and stuffs.