The rate of change of the hypotenuse after 2 minutes is 0.505 cm/min
Let L be the length of one leg and D be the length of the other leg of the right triangle and y its hypotenuse
Since it is a right angled triangle, we have that, using Pythagoras' theorem
y² = L² + D²
Since the length of sides are the same, L = D = 70 cm.
So, y² = L² + D²
y² = 70² + 70²
y² = 2(70²)
y = 70√2
y = 98.99 cm
Also, one side increases at a rate of 5 cm/min and the other side decreases at a rate of 5 cm/min.
The increase in length of one side after 2 min is 5cm/min × 2 min = 10 cm.
So, it new length is L' = 70 + 10 = 80 cm
The decrease in length of the other side after 2 min is -5cm/min × 2 min = -10 cm.
So, it new length is D' = 70 + (-10 cm) = 60 cm
So, the new hypotenuse length is y' = √(L'² + D'²)
= √(80² + 60²)
= √(6400 + 3600)
= √10000
= 100 cm
Now, the change in length of the hypotenuse side in 2 minutes is Δy = 100 cm - 98.99 cm = 1.01 cm
So, rate of change of the hypotenuse after 2 minutes is 1.01 cm/2 min = 0.505 cm/min
The rate of change of the hypotenuse after 2 minutes is 0.505 cm/min
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