If the sum of base and height of a right triangle is 20 cm, what is the maximum area of the triangle?

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Answer 1 · 2017-07-08T11:40:59

The maximum area is #=50cm^2#

Let the base be #=xcm# and

The height is #=(20-x) cm#

The area is

#A=1/2*x*(20-x)#

#A=10x-1/2x^2#

We derive wrt #x#

#(dA)/dx=10-x#

The max. or min. is when

#(dA)/dx=0#

#10-x=0#, #=>#, #x=10#

The maximum is when #x=10#

The area is #A=1/2*10*10=50cm^2#

graph{10x-1/2x^2 [-41.2, 75.83, -3.84, 54.7]}

Answer 2 · 2017-07-08T12:49:57

#50" square cm"#

#"the maximum area occurs when the base and height are"#
#"equal "#

#"that is when " b=h=10#

#rArr"max. area " =1/2bh=1/2xx10xx10=50" square cm"#