Figure 2-6.—"Stepping off" with a framing square.the tongue and the blade even with the edge of the board.Draw the pencil marks as shown. The distance betweenthese marks, measured along the edge of the board, isthe length of the hypotenuse of a right triangle with theother sides each 12 inches long. You will find that thedistance, called the bridge measure, measures just under17 inches—16.97 inches, as shown in the figure. Formost practical Builder purposes, though, round 16.97inches to 17 inches.Solving for Unit and Total Run and RiseIn figure 2-5, the problem could be solved by asingle set (called a cut) of the framing square. This wasdue to the dimensions of the triangle in question lyingwithin the dimensions of the square. Suppose, though,you are trying to find the length of the hypotenuse of aright triangle with the two known sides each being 48inches long. Assume the member whose length you aretrying to determine is the brace shown in figure 2-6. Thetotal run of this brace is 48 inches, and the total rise isalso 48 inches.To figure the length of the brace, you first reducethe triangle in question to a similar triangle within thedimensions of the framing square. The length of thevertical side of this triangle is called unit of rise, and thelength of the horizontal side is called the unit of run. ByFigure 2-7.–"Stepping off" with a square when the unit of runand unit of rise are different.a general custom of the trade, unit of run is always takenas 12 inches and measured on the tongue of the framingsquare.Now, if the total run is 48 inches, the total rise is 48inches, and the unit of run is 12 inches, what is the unitof rise? Well, since the sides of similar triangles areproportional, the unit of rise must be the value of x inthe proportional equation 48:48::12:x. In this case, theunit of rise is obviously 12 inches.To get the length of the brace, set the framing squareto the unit of run (12 inches) on the tongue and to theunit of rise (also 12 inches) on the blade, as shown infigure 2-6. Then, “step off” this cut as many times as theunit of run goes into the total run. In this case, 48/12, or4 times, as shown in the figure.In this problem, the total run and total rise were thesame, from which it followed that the unit of run andunit of rise were also the same. Suppose now that youwant to know the length of a brace with a total run of 60inches and a total rise of 72 inches, as in figure 2-7. Sincethe unit of run is 12 inches, the unit of rise must be thevalue of x in the proportional equation 60:72::12.x. Thatis, the proportion 60:72 is the same as the proportion12:x. Working this out, you find the unit of rise is2-5

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