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Home > PC > Chapter 2 > Lesson 2.3.5 > Problem 2-133


Square of area cm2 has the largest possible equilateral triangle inscribed in it. The triangle has vertices , , and , where E is between and , and is between and .

Rectangle, A B C D, with point e, about 1 fourth from vertex b, on side, B C, & point f, about 1 fourth from vertex d, on side C D, & shaded triangle, A E F.

  1. Why is ?

    In answering these questions, think about the degree measures of the angles.
    Label the interior angles of the equilateral triangle.

  2. Why is isosceles?

    Find and label the base angles of the isosceles triangle.

  3. Find the area of triangle .

    Find the angles in triangle . Then use a trig function to find a side of the equilateral triangle.
    Then find the height of the equilateral triangle. At that point, you can use the formula: .

Angles added to triangle, A E F, each angle is 60 degrees.

Label added to angle, E F C, 45 degrees.