Triangle MRN is created when an equilateral triangle is folded in half.

4√3 units

Explanation:

Triangle MRN is created when an equilateral triangle is folded in half. What is the value of y?

A. 2√3 units

B. 4 units

C. 4√3 units

D. 8 units

Solution:

Pythagoras theorem states that for a right angled triangle, the square of its hypotenuse is equal to the sum of the square of the other two legs of the triangle. The hypotenuse is the longest side (that is side opposite to the 90 degrees).

In triangle SRM, using Pythagoras:

x² = z² + 2²

z² = x² - 2²

In triangle SRN, using Pythagoras:

y² = z² + 6²

substituting z² = x² - 2²:

y² = x² - 2² + 6²

In triangle RMN, using:

(6 + 2)² = y² + x²

substituting y² = x² - 2² + 6²:

8² = x² - 2² + 6² + x²

64 = 2x² - 4 + 36

64 = 2x² + 32

2x² = 32

x² = 16

x = 4

y² = x² - 2² + 6² = (4)² - 2² + 6²

y² = 16 - 4 + 36

y² = 48

y = 4√3

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