# math

A carpenter is building rectangular walls for a room addition. The width of a section of wall is two times the height h. Each section has a brace that connects two opposite corners of the section. What is a simplified expression for the length of a brace?

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1. Is this written correctly? Usually the height is longer than the width! Again, draw a picture. Another right triangle.
Let x = height; let 2x = width. Using Pythagorean Theorem:
hyp^2 = x^2 + (2x)^2
hyp^2 = x^2 + 4x^2
hyp^2 = 5x^2
take square root of each side:
hyp = x * sqrt(5)

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