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Maximize area of triangle question

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Maximize area of triangle question [#permalink] New post 10 Jun 2013, 01:24
So if we have 2 sides of a triangle 5 and 8 to maximize the triangle it has to be a right triangle? If we have to find the hypotenuse of this triangle

it would be X^2 = 5^2 + 8^2 ( why does it have to be in this particular order?)

can the numbers be interchanged,i.e. 8^2 = 5^2 + x^2

I hope I've made some sense lol kindly help out. Thanks!

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Re: Maximize area of triangle question [#permalink] New post 10 Jun 2013, 01:46
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fozzzy wrote:
So if we have 2 sides of a triangle 5 and 8 to maximize the triangle it has to be a right triangle? If we have to find the hypotenuse of this triangle
it would be X^2 = 5^2 + 8^2 ( why does it have to be in this particular order?)
can the numbers be interchanged,i.e. 8^2 = 5^2 + x^2
I hope I've made some sense lol kindly help out. Thanks!


Hi fozzzy!

The general formula of Area can be considered as Area = (1/2)*ab sin C where C is the included angle.
The maximum would clearly be when sin C = 1 i.e. C=90 degrees. Hence a right angled traingle, as you have rightly mentioned.

For a traingle of given sides, 5 and 8, we can certainly assume that 8 be the hypotenues or we can assume 5,8 be the sides. In both the cases, we have to find which actually yeilds the max area. Incase 8 is the hypotenues, the base comes out to be approx 6 and the area is approx 15. But when 8 and 5 are the sides, the area is 20. Hence, the case where 8 and 5 are assumed sides, the area appears to be maximized. Hence we can assume the same if we are considering maximum area.

Hope it clarifies your doubt! :)

Regards,
A

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Re: Maximize area of triangle question [#permalink] New post 10 Jun 2013, 04:16
so it seems a better option to plug the numbers and solve to get the hypotenuse rather than substituting one of the numbers as the hypotenuse...

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Re: Maximize area of triangle question [#permalink] New post 10 Jun 2013, 20:42
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fozzzy wrote:
so it seems a better option to plug the numbers and solve to get the hypotenuse rather than substituting one of the numbers as the hypotenuse...


Yes, because longer the legs of the right triangle, more the area. If legs are 5 and 8, area will be more than the situation in which the legs are 5 and 6. The important point is not how to get the hypotenuse but why to get it that way.

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Re: Maximize area of triangle question   [#permalink] 10 Jun 2013, 20:42
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