Answer:
-1 8/9 cm/min
Step-by-step explanation:
The area of a triangle is given by ...
A = (1/2)bh
Then when the area is 81 cm² and the altitude is 9 cm, the base is ...
81 cm² = (1/2)(b)(9 cm)
(81 cm²)/(4.5 cm) = b = 18 cm
Differentiating the area formula implicitly, you have ...
A' = (1/2)(b'h +bh')
Fill in the given values and solve for b':
5 cm²/min = (1/2)(b'(9 cm) +(18 cm)(1.5 cm/min))
5 cm²/min = b'(4.5 cm) +13.5 cm²/min . . . . simplify
Subtract 13.5 and divide by the coefficient of b':
(-8.5 cm²/min)/(4.5 cm) = b' = -1 8/9 cm/min
The base is changing at the rate of -1 8/9 ≈ -1.889 cm per minute.
