Answer:
The area is changing at the point of [tex]\mathbf{61200 m^2/year}[/tex]
Step-by-step explanation:
From the given information:
Let's recall from our previous knowledge that the formula for finding the area of a rectangle = L × w
where;
L = length and w = width of the rectangle
Suppose the Length L is twice the width w
Then L = 2w --- (1)
From The area of a rectangle
A = L × w
A = 2w × w
A = 2w²
Taking the above differentiating with respect to time
[tex]\dfrac{dA}{dt }= 4w \times \dfrac{dw}{dt} --- (2)[/tex]
At the time t
[tex]\dfrac{dw}{dt}= 34 m \ per \ year ; w = 450 \ m[/tex]
Replacing the values back into equation 2, we get:
[tex]\dfrac{dA}{dt }= 4 \times 450 \times 34[/tex]
[tex]\mathbf{\dfrac{dA}{dt }= 61200 m^2/year}[/tex]
