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Two sides of a right angle triangle are made of 10 cm wire, and the longest side is a riverbank. the required area is 20cm^2.

a, find the expression for the right angle triangle in terms of x
b, is it possible to optimize the fencing?

User Alex Yan
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1 Answer

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a. The expression for the right triangle is x² - 10x - 40 = 0

b. Yes, It is possible to optimize the fencing

How to find the expression

Let the two sides of the right-angled triangle be x and y

a. Expression for right angle triangle

Area = 1/2 * x * y

base is x and the height is y

20 = xy/2

xy = 40

j

And x + y = 10, y = 10 - x

x(10 - x) = 40

10x - x² = 40

x² - 10x - 40 = 0

To optimize the fencing means to find the value of x that minimizes or maximizes the area A.

To do this, you can take the derivative of the area expression with respect to x, set it equal to zero, and solve for x.

User Amiabl
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