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If length of three sides of a trapezium other than base are eq

Question

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

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Text solutionVerified

Solution:

A = x \frac{y}{2} + 10 y + x \frac{y}{2}

= x y + 10 y

A = x 100 - x^{2} + 10 100 - x 2

= \frac{x + 10}{U} \frac{100 - x ^{2}}{V}

d \frac{A}{d x} = 1 (100 - x^{2}) + \frac{x - 10}{2 100 - x ^{2}} (- 2 x)

d \frac{A}{d x} = 0

- \frac{100 - x ^{2} - x ^{2} - 10 x}{100 - x ^{2}} = 0

- (2 x^{2} + 10 x - 100) = 0

- 2 (x^{2} + 5 x - 50)

(x + 10) (x - 5) = 0

x = - 10

x = - 5

A = x y + 10 y

15100 - 25

= 753 c m^{2}

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Question Text	If length of three sides of a trapezium other than base are equal to 10cm, then find the area of the trapezium when it is maximum.
Answer Type	Text solution:1
Upvotes	150