The legs of an isosceles right triangle increase in length at a rate of 6 m divided by s.a. At what rate is the area of the triangle changing when the legs are 4 m​ long?b. At what rate is the area of the triangle changing when the hypotenuse is 6 m​ long?c. At what rate is the length of the hypotenuse​ changing?

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Asked Nov 25, 2019
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The legs of an isosceles right triangle increase in length at a rate of 6 m divided by s.
a. At what rate is the area of the triangle changing when the legs are 4 m​ long?
b. At what rate is the area of the triangle changing when the hypotenuse is 6 m​ long?
c. At what rate is the length of the hypotenuse​ changing?

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Step 1

Let x  be the length of leg and h be the length of hypotenuse of an isosceles right triangle. Then we have

 

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dx 6m/s dt

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Step 2

Now, We know that Area of right angled triangle is 1/2 of product of length of legs , so we have

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1 A = dxc = x- dc dA dt x = 4m dA =4x6 24m2/s dx

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Step 3

If length of hypotenuse is 6m, then we c...

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h 6m x* = 6 r = 3m Вт

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Tagged in

Math

Calculus

Derivative