The altitude of a triangle is increasing at a rate of 3.0 centimeters/minute while the area of the triangle is increasing at a rate of 2.0 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 11.5 centimeters and the area is 91.0 square centimeters?

Question

The altitude of a triangle is increasing at a rate of  3.0 centimeters/minute while the area of the triangle is increasing at a rate of  2.0 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 11.5 centimeters and the area is  91.0 square centimeters?

anonymous · Answer

$\large A=\frac{1}{2}bh \rightarrow A'=\frac{1}{2}(b'h+bh')$

since h=11.5 and A=91, you can find b.

then you can replace all those other given values to find b' (the rate at which the base is changing)...

anonymous · Answer

i tried but i kept getting the wrong answer

anonymous · Answer

what did you get for b ???

anonymous · Answer

15.82

anonymous · Answer

the base is decreasing at 3.78 cm/min is incorrect?

anonymous · Answer

its coming up as incorrect

anonymous · Answer

ok... lesseee....

anonymous · Answer

$\large A'=\frac{1}{2}(b'h+bh') \rightarrow b'=\frac{2A'-bh'}{h} $

anonymous · Answer

91 = (1/2)*(b)*(11.5)
so b = 15.826

now...
A' = 2
b = 15.826
h' = 3
h = 11.5

anonymous · Answer

hmmm... i still got b' = -3.781 cm/min...

anonymous · Answer

ohh i missed the neg sign

anonymous · Answer

it worked out now thanks!

anonymous · Answer

yw... 
btw... my first answer was positive because I said the base is "decreasing at 3.78 cm/min" this is also correct.

anonymous · Answer

yeah now that i reread it i understood

anonymous · Answer

great.... :)

anonymous · Answer

and that is something to watch out for with these related rates problems.....

anonymous · Answer

im posting another problem that i am having trouble with, do you mind checking it out to see if you can help

anonymous · Answer

yeah... no prob....