What is the number of different squares which can be inscribed in a given equilateral triangle?

  1. 👍 0
  2. 👎 0
  3. 👁 158
  1. If we lay one side along the x-axis, and one vertex at (0,0), and let the side be of length 1, the triangles sides can be written as


    Assuming the obvious position where one side of the square lies along one side of the triangle, from (a,0) to (2a,0), and

    √3x = a
    √3(1-x) = √3 - 2a = a
    which gives us a square of side 1/√3.
    There are 3 sides to the triangle, giving us 3 identical squares.

    Now, any other inscribed square must have a vertex on each side of the triangle, so if we pick any point (a,0) we must have lines

    y = m(x-a)+b
    y = (-1/m)(x-a)+c
    where the sides from (a,0) to the other two sides of the triangle are of equal length.

    So, set up your equations of the intersecting lines, and the distances, and fire away. I have no idea whether the squares will be of the same size as above. If not, then there are an infinite number of different squares possible.

    I haven't yet come up with a solution using just geometry.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Geometry

    Let ABC be any triangle. Equilateral triangles BCX, ACY, and BAZ are constructed such that none of these triangles overlaps triangle ABC. a) Draw a triangle ABC and then sketch the remainder of the figure. It will help if

  2. Math

    Can someone please check to see if I answered these true and false statements correctly? Thank you! 1. A triangle can have two right angles. (TRUE??) 2. An equilateral triangle is also an acute. (TRUE??) 3. A right triangle can

  3. Geometry

    Which step is the same when constructing an inscribed square and an inscribed equilateral triangle? A.Connect every arc along the circle. B.Construct a circle of any arbitrary radius. C.Set the compass width to greater than half

  4. geometry

    an equilateral triangle of side 20cm is inscribed in a circle.calculate the distance of a side of the triangle from th centre of the circle.

  1. math

    an equilateral triangle of side 20cm is inscribed in a circle calculate the distance of a side of the triangle from the centre of the circle

  2. geometry

    An isosceles triangle has two 10.0-inch sides and a 2w-inch side. Find the radius of the inscribed circle of this triangle, in the cases w = 5.00, w = 6.00, and w = 8.00. Then Write an expression for the inscribed radius r in

  3. math

    An equilateral triangle is inscribed in a circle. The radius of the circle is 21 in. Determine the side length of the triangle to the nearest 10th of an inch

  4. math

    an equilateral triangle of side 10cm is inscribed in a circle. find the radius of the circle? show the solution

  1. geometry

    Rewrite the statement in if-then form. All equilateral triangles have three congruent sides. a. a figure has three congruent sides if and only if it is an equilateral triangle. b. a figure is an equilateral triangle if and only if

  2. Math

    Which triangle is not possible to construct? A a right isosceles triangle B an acute equilateral triangle C an obtuse scalene triangle D a right equilateral triangle I have no idea what the answer is, pls help me

  3. 10th grade

    Triangle ABC is an equilateral triangle.AD=10 What is the length of CD? Give your answer to the nearest whole number.

  4. Algebra 2

    Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Find the sum of a finite geometric series. The sides of an equilateral triangle measure 16 inches. The midpoints of the

You can view more similar questions or ask a new question.