Question

Consider a rectangle with dimensions x and y in cm. If x Is growing at a rate of 2 cm/s and y is growing at a rate of 3 cm/s, find the rate at which the length of the diagonal is changing when x= 5 cm and y= 8 cm.

Answer 1

dc/dt = 3.6cm/s

Step-by-step explanation:

Let c be the length of the diagonal:

`c=√(x^2+y^2)` The rate at which c is changing is:

`(dc)/(dt) =(2*x*(dx)/(dt) +2*y*(dy)/(dt))/(2*√(x^2+y^2) )`

where:

x=5cm dx/dt=2cm/s

y=8cm dy/dt=3cm/s

`(dc)/(dt) =3.6cm/s`