Find the Max Area of a Right Triangle with Hypotenuse

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Question: calc. area. triangle
Find the maximal area of a right triangle with hypotenuse of length 8.

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Answered By:

Ethan S.
Experienced Ivy League Math and Computer Science Tutor

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We can also just use trigonometry. Let the angles be 90 degrees, A and 90-A. Base=cosA and height=sinA, thus area =0.5(8)sinA(8)cosA
Now by AM-GM inequality, sinAcosA<=1/2
Taking the minimum value, we get minimum area=0.5×0.5×8×8
=64/4
=16

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thank you so much ! you just saved me for my exam tomorrow !

mabelespinoza