A complete and practical solution book for the common school teacher . 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. FIG. 93. Solution. (1) Let ABCD represent the lot; HGLE, the path. (2) EI, HS, GF and LK are each perpendicular toDB, and are each 18 in. (3) By similar triangles, DC : CB :: DS : HS,and DS = ft. (4) DC :CB::GF: FB, from which FB—1 ft. (5) The total area of the four triangles is sq. ft. (6) DC2 + BC* = DB2, from this we f
A complete and practical solution book for the common school teacher . 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. FIG. 93. Solution. (1) Let ABCD represent the lot; HGLE, the path. (2) EI, HS, GF and LK are each perpendicular toDB, and are each 18 in. (3) By similar triangles, DC : CB :: DS : HS,and DS = ft. (4) DC :CB::GF: FB, from which FB—1 ft. (5) The total area of the four triangles is sq. ft. (6) DC2 + BC* = DB2, from this we find DB=+ ft. (7) 593 23 ft.—3 25 ft. (DS+1) =+ ft., SFor IK. (8) ft. =+ sq. ft., area of the two rectangles. (9) sq. ft.+ sq. ft. = sq. ft., total area. PROBLEM 414. Find the diagonal of a rectangular field containing lHi A., is to its breadth as 12 to 5. Solution.
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