A complete and practical solution book for the common school teacher . the 19-| A. is taken above the line 70-^-20=31 +3£2:.-. PF= ch. , we will take it below the line is evident that the line PF will fall below its present position, as PFr shown in the figure. (11) Now, the quadrilateral PABF contains 19| A. (12) DPEC+PABF=35| A. (13) PEF=40 A.—35i £ A. (14) Then, the right triangle PEF = 4| A. (15) 4|X2 = 9 A., or 90 sq. ch., area of the rectangle PEFS. (16) EE=90-^20 = 4ich.; that is, the area of a rectangle di- vided by its length gives its width, or vice vers
A complete and practical solution book for the common school teacher . the 19-| A. is taken above the line 70-^-20=31 +3£2:.-. PF= ch. , we will take it below the line is evident that the line PF will fall below its present position, as PFr shown in the figure. (11) Now, the quadrilateral PABF contains 19| A. (12) DPEC+PABF=35| A. (13) PEF=40 A.—35i £ A. (14) Then, the right triangle PEF = 4| A. (15) 4|X2 = 9 A., or 90 sq. ch., area of the rectangle PEFS. (16) EE=90-^20 = 4ich.; that is, the area of a rectangle di- vided by its length gives its width, or vice versa. MENSURA TION. 205 (17) PF=V202+4£ PF= ch. PROBLEM 407. In a square field which contains 10 A., a line is drawn from thesouthwest corner to the middle of the north side; from the southeastcorner to the middle of the north side; and from the southwest cornerto the northeast corner: find the area of the triangle enclosed by thethree lines. Solution. (1) (2) (3) Let ADEF be the side DE is easily found to be is40 rd., or (4) (5) (6)(7). V (10X160).The area of the triangle BEF is 20x40^2, or 400 sq. rd., which is also the area of the triangle ABE, for it has the same base BE and the same alti-tude the area of the triangle BEC from this, and the result is the area BE is half AF, the altitude of the triangle BCE half the altitude of the similar triangle ACF, forBE : AF :: BC : CF :: EC : AC :: GC : *. The altitude of the triangle is equal to \ of 40, or 13^ rd., and its area is 20X13J-J-Hence, 400—133J = 266f sq. rd ABC. FIG. IS or 1334the 5 sq. of the triangle PROBLEM 408. A man takes for himself a central square of 40 acres, within asquare of 160 acres, and gives to his four sons rectangular farms equalin every respect and making up the remainder of the farm. The fatherand sons are to have dwellings centrally located in their respectivefarms: how far will each son be from his nearest brother, and from hisfat
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