A complete and practical solution book for the common school teacher . FIG. 91. PROBLEM 412. Required the length of a piece of carpet that is a yard wide, withsquare ends, that can be placed diagonally in a room 40 ft. long and 30ft. wide, the corners of the carpet just touching the walls. Solution. (1) Let ABCD be the room, and GFEH the strip ofcarpet. (2) Let *=EC=AG, and y= CF = AH. (3) Then, by similar triangles, 40—x : 30—y :: y : x. (4) Or, 40*—*2 = 30?/—y* . (1). (5) We also have *2+i/2=32, or*=V(9-:y2) • • (2), (6) Substituting in (1) and reducing, y±—30j3+616>2+135jj/ — .
A complete and practical solution book for the common school teacher . FIG. 91. PROBLEM 412. Required the length of a piece of carpet that is a yard wide, withsquare ends, that can be placed diagonally in a room 40 ft. long and 30ft. wide, the corners of the carpet just touching the walls. Solution. (1) Let ABCD be the room, and GFEH the strip ofcarpet. (2) Let *=EC=AG, and y= CF = AH. (3) Then, by similar triangles, 40—x : 30—y :: y : x. (4) Or, 40*—*2 = 30?/—y* . (1). (5) We also have *2+i/2=32, or*=V(9-:y2) • • (2), (6) Substituting in (1) and reducing, y±—30j3+616>2+135jj/ — . (3). (7) /=, *= (8) Hence, the length is V (40—x) a + (30—^)a =+ ft. Note.—This solution was prepared by the author forthe^m<?r*Va«Mathematical PROBLEM 413. What is the area of a path 1 yard wide, passing diagonally acrossa lot 20 rd. wide and 30 rd. long, the diagonal of the lot passingthrough the middle of the path? MENSURA TION. 209
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