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If the length of three sides of a trapez...

If the length of three sides of a trapezium other than the base is 10cm each, find the area of the trapezium, when it is maximum.

Text Solution

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`A=xy/2+10y+xy/2`
`=xy+10y`
`A=xsqrt(100-x^2)+10sqrt(100-x2)`
`=(x+10)/U(sqrt100-x^2)/V`
`dA/dx=1(sqrt100-x^2)+(x-10)/(2sqrt100-x^2) (-2x)`
`dA/dx=0`
`-(100-x^2-x^2-10x)/sqrt(100-x^2)=0`
`-(2x^2+10x-100)=0`
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