Answer to Question #286262 in Chemistry for levi

Question

The sides of a triangle measuring 40 m, 32 m, and 16 m increase at the rates of 2 m/s, 5 m/s, and 3 m/s, respectively. How fast is the area of the triangle changing?

a. 138.42 m^2/s

b. 113.69 m/s

c. 127.33 m^2/s

d. 113.69 m^2/s

Answer 1

S = (p x (p-a) x (p-b) x (p-c))^1/2

p₁ = (a + b + c) / 2 = (40 + 32 + 16) / 2 = 44

S₁ = (44 x (44-40) x (44-32) x (44-16))^1/2 = 243.2 cm²

p₂ = (42 + 37 + 19)/2 = 49

S₂ = (49 x (49-42) x (49-37) x (49-19))^1/2 = 351.4 m²

deltaS = 351.4 - 243.2 = 113.7 m²

Answer d. 113.69 m²/s