Physics
An equilateral triangle initially has side length equal to 17 cm. Each vertex begins moving in a straight line towards the midpoint of the opposite side at a constant rate of 2.3 cm/s, continuously forming progressively smaller equilateral triangles until it disappears. At what rate is the area of the triangle decreasing at the instant it vanishes? The area A of an equilateral triangle with side length s is
A= (sqrt(3)/4)(s^2)

dA/ds = sqrt 3 (1/2) s
dA/dt = .5 sqrt 3 sds/dt
but
altitude h = (s/2) sqrt 3
dh/dt = .5 sqrt 3 ds/dt
so
ds/dt = [2/sqrt 3] dh/dt
dA/dt=.5 sqrt 3*[2/sqrt 3]s dh/dt
= s dh/dt
evaluate when s = 17 and dh/dt = 2.3posted by Damon

whoa, at the instant it vanished?
dA/dt = s dh/dt
as s > 0 and dh/dt is constant
dA/dt > 0posted by Damon

wow got to right the question and solution down
posted by collins
Respond to this Question
Similar Questions

Math
A pentagon is formed by putting together three identical equilateral triangles and one larger equilateral triangle with length of edge equal to 2 times that of the smaller equilateral triangle. If the perimeter of the smaller 
Maths
An equilateral triangle with side length 33 is divided into 33^2 smaller unit equilateral triangles each with side 1, forming a triangular lattice. We color each segment of length 1 either Red, Blue or Green, subject to the 
Maths
An equilateral triangle with side length 33 is divided into 33^2 smaller unit equilateral triangles each with side 1, forming a triangular lattice. We color each segment of length 1 either Red, Blue or Green, subject to the 
mathematics
An equilateral triangle with side length 33 is divided into 332 smaller unit equilateral triangles each with side 1, forming a triangular lattice. We color each segment of length 1 either Red, Blue or Green, subject to the 
geometry
f equilateral triangle JKL is cut by three lines as shown above to form four equilateral triangles of equal area, what is the length of a side of one of the smaller triangles? 
geometry and combinatorics
An equilateral triangle with side length 33 is divided into 33^2 smaller unit equilateral triangles each with side 1, forming a triangular lattice. We color each segment of length 1 either Red, Blue or Green, subject to the 
Algebra
The perimeter of an equilateral triangle is 7 in. more than the perimeter of a square. The side of the triangle is 5 in. longer than the side of the square. Find the length of each side of the triangle. (Note: An equilateral 
Analytic Geometry
The line segment joining a vertex of a triangle and the midpoint of the opposite side is called the median of the triangle. Given a triangle whose vertices are A(4,4), B(10, 4) and C(2, 6), find the point on each median that is 
grade six math
Draw an equilateral triangle. Divide each side in half and join the points to make four small equilateral triangles. Rearrange these four equilateral triangles into a parallelogram. Compare the perimeter of the original triangle 
Math
An equilateral triangle s divided into 4 congruent equilateral triangles. What method can be used to find the area of the larger equilaterl triangle give the area of one of the smaller triangles? F. Multiply the area of the larger