A complete and practical solution book for the common school teacher . FIG. 102. PROBLEM 429. On a rectangular lot whose sides are 39 ft. and 49 ft., a house isbuilt, covering- 999 sq. ft.; the house is so located and of such a shape,that the lot surrounding- the house is of uniform width: find the basaldimensions of the house. [Helfrich.) Solution. (i) (2)(3). Let ABCD represent the rectangular lot and SK the the lot into four equal parts as represented in Fig. 103, and arrange these four figures as shown in Fig. 104, which makes the square | ft., and CR = 19£ ft. (4) The
A complete and practical solution book for the common school teacher . FIG. 102. PROBLEM 429. On a rectangular lot whose sides are 39 ft. and 49 ft., a house isbuilt, covering- 999 sq. ft.; the house is so located and of such a shape,that the lot surrounding- the house is of uniform width: find the basaldimensions of the house. [Helfrich.) Solution. (i) (2)(3). Let ABCD represent the rectangular lot and SK the the lot into four equal parts as represented in Fig. 103, and arrange these four figures as shown in Fig. 104, which makes the square | ft., and CR = 19£ ft. (4) Then, the side of the square HN = 19^4-24^=44 ft. (5) The area of HP=442=1936 sq. ft. MEN SURA TION. 217 (6) The area of the lot DB = 49x 39 = 1911 sq. ft. (7) The area of the lot surrounding the house is 1911—999 = 912 sq. ft. (8) 1936—912 = 1024 sq. ft., area of the square DE. (9) DF = V1024 = 32ft. (10) (44—32)^-2 = 6 ft. = ZX, the width of the lot. (11) ZX = TK. From this we can see that the width of the house is 39 ft.—12 ft., and the length 49 ft.— ft. PROBLEM 430. My lot contains 135 sq. rd., and the breadth is to the length as 3 to5: what is the width of a road which shall extend from one corner halfaround the lot and occupy \ of the ground? (R. H. A.) Solution. (1) From Figs. 103 and 104, let AC represent the lot con- tai
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