A complete and practical solution book for the common school teacher . then have y* + 2xy + x2 + 24(x + r) = 1225, or(x+y)* + 24(x+y) = 1225. (6) Completing the square, x? + y = 25 . . (3). 144 (7) ;r = — from (2), and substitute its value in (3), whence, ) 25 r = —144. (8) y — 12| = ±3it or j = 16 or 9, and x = 9 or 16. .. The base is 21 ft., or 28 ft., and the perpendicular is28 ft., or 21 ft. PROBLEM 320. The perimeter of a rig-ht triangle is 24; the hypothenuse is 2 longerthan the altitude, and the altitude 2 longer than the base: what are itssides? Solution. (1) Let ABC be the triangle, a
A complete and practical solution book for the common school teacher . then have y* + 2xy + x2 + 24(x + r) = 1225, or(x+y)* + 24(x+y) = 1225. (6) Completing the square, x? + y = 25 . . (3). 144 (7) ;r = — from (2), and substitute its value in (3), whence, ) 25 r = —144. (8) y — 12| = ±3it or j = 16 or 9, and x = 9 or 16. .. The base is 21 ft., or 28 ft., and the perpendicular is28 ft., or 21 ft. PROBLEM 320. The perimeter of a rig-ht triangle is 24; the hypothenuse is 2 longerthan the altitude, and the altitude 2 longer than the base: what are itssides? Solution. (1) Let ABC be the triangle, and AG the square ofthe hypothenuse, ASthe square of the alti-tude, and AK the .squareof the base. (2) The rectangles nn and AX, etc., are equal. (3) The two rectangles nn and the three squaresaaa = the square onthe base. (4) The square of the base — nn! = aaa = k, orany of the rectangles, or 12; then the length of the rect-angles = the length of the base. (5) Also the area of one of the rectangles k is 12, and one side is four less than the other FIG. 18. 148 FAIRCHILDS SOLUTION BOOK. (6) Then by Fig. 19, let WZ be a straight line equal to thedifference of the sides ofthe rectangle k. (7) Upon WZ as a diameter de- scribe a circle, and at theextremity of the diameterdraw the tangent WF equalto the side of a square hav-ing the same area as therectangle h. (8) Through the point F and the center O, draw the se-cant FQ; then will FY,FQ be the adjacent sidesof the rectangle. WF = V12 = WZ = 4, and WO FO
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