Question

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How do you solve

Answer 1

`y=4√(3)\ units`

Explanation:

Triangle MRN is created by folding an equilateral triangle by half. Since triangle MRN is right triangle, the equilateral triangle must be folded along the height drawn to one side.

In equilateral triangle with side length of a units, the height is
`(a√(3))/(2)\ units` and the height is greater than half the side because

`(a√(3))/(2)>(a)/(2).`

The leg with length x units has the smaller projection (2 units long) than the leg with length y units has (6 units long).

This means the leg with length y units is the height of the equilateral triangle. If the leg with length y units is the height of the equilateral triangle, then the hypotenuse MN = 8 units is the side of the equilateral triangle and lex with length x units is half the side, so x = 4 units.

By the Pythagorean theorem,

`y^2=8^2-4^2\\ \\y^2=64-16\\ \\y^2=48\\ \\y=4√(3)\ units`