Question

A ladder AB of 10 mts long moves with its ends on the axes. When the end A is 6 mts from
origin, it moves away from it at 2mts/minute. The rate of increase of the area of the OAB
sq.mts/min​

Answer 1

Step-by-step explanation:

Given  

A ladder AB of 10 mts long moves with its ends on the axes. When the end A is 6 mts from origin, it moves away from it at 2 mts/minute . The rate of increase of the area of the OAB  sq.mts/min​

• We know that area of triangle = 1/2 x base x height
•                       Triangle  OAB = 1/2 x OA. OB
•                                            OA^2 + OB^2 = 10^2
•                                 So        6^2 + OB^2 = 100
•                                                 OB^2 = 100 – 36
•                                                 OB^2 = 64
•                                                 OB = 8
• Now d / dt (OA) = 2 m / min
• Also d/dt (OB) = OA / OB d(OA) / OB
• Therefore d/dt AOAB = 1/2 OA d/dt (OB) + 1/2 OB d/dt (OA)
•                      d/ dt (AO AB) = 1/2 (- 36/ 8 + 8) x 2
•                                              = 1/2 (28 / 8) x 2
•                                              = 28/8
•                                               = 7/2