- #1
syeh
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Homework Statement
An equilateral triangle with side length x sits atop a rectangle with a base length of x, with the base of the triangle coinciding with the top base of the rectangle. the height of the rectangle is 7 times the length of its base. If the combined area of the figures is increasing at a rat of 8 mm^2/sec, find the rate at which a side of the triangle is lengthening at the moment the base of the rectangle is 20 mm.
The Attempt at a Solution
so i started by making a sketch. (I attached a sketch of the figures). then, i found the Area and then dA/dt:
A=lw+1/2 bh
=(7x)(x)+ 1/2 (x)((x*sqrt3)/2)
=7x^2 + (x^2*sqrt3)/4
dA/dt= 14x dx/dt + (x*sqrt3)/2 dx/dt
then, plug in x=20 mm, and dA/dt=8 mm^2/min:
8= 40 dx/dt + 2.474 dx/dt
8= dx/dt (40+2.474)
8= dx/dt (42.474)
dx/dt = 0.188 mm^2/sec