Asked by Grace
The area of a triangle is growing at a rate of 4 cm2/min. If the height of this triangle is always twice the base, find the rate of change of the base when the base is 6cm.
Answers
Answered by
mathhelper
let the base be x cm
then the height is 2x cm
Area = (1/2)(base)(height)
= (1/2)(x)(2x) = x^2
d(Area)/dt = 2x dx/dt
given: d(area)/dt = 4 cm^2 / min
find : dx/dt when x = 6 cm
4 = 2(6) dx/dt
dx/dt = 1/3 cm/min
then the height is 2x cm
Area = (1/2)(base)(height)
= (1/2)(x)(2x) = x^2
d(Area)/dt = 2x dx/dt
given: d(area)/dt = 4 cm^2 / min
find : dx/dt when x = 6 cm
4 = 2(6) dx/dt
dx/dt = 1/3 cm/min
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