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)

asked by Anonymous
  1. 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 = -2.3

    posted by Damon
  2. whoa, at the instant it vanished?

    dA/dt = s dh/dt
    as s ---> 0 and dh/dt is constant
    dA/dt ---> 0

    posted by Damon
  3. wow got to right the question and solution down

    posted by collins

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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?
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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

More Similar Questions