Consider a rectangle whose length is increasing at the uniform rate of 2 m / sec , breadth is decreasing at the uniform rate of 3 m / sec and the area is decreasing at the uniform rate of 5 m 2 / sec

Question

Consider a rectangle whose length is increasing at the uniform rate of 2 m / sec , breadth is decreasing at the uniform rate of 3 m / sec and the area is decreasing at the uniform rate of 5 m 2 / sec . If after some time the breadth of the rectangle is 2 m then the length of the rectangle is

TestHub · Accepted Answer

Let A be the area, b be the breadth and ℓ be the length of the rectangle. Given: d t d A ​ = − 5 , d t d ℓ ​ = 2 , d t d b ​ = − 3 We know, A = ℓ × b ​ ⇒ d t d A ​ = ℓ ⋅ d t d b ​ + b ⋅ d t d ℓ ​ = − 3 ℓ + 2 b ⇒ − 5 = − 3 ℓ + 2 b . ​ When b = 2 , we have − 5 = − 3 ℓ + 4 ⇒ ℓ = 3 9 ​ = 3 m

Mathematics - Application of Derivative Question with Solution | TestHub

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