A complete and practical solution book for the common school teacher . are of the diagonal of a square is equal totwice the square of one side, or twice the square itself. MENSURATION. 203 PROBLEM area of a square is 800 sq. ft.: what is the diagonal? Solution. (1) 800 sq. ft. = area of the square. (2) 800x2 = 1600 sq. ft., double the area. (3) v 1600 = 40 ft., the diagonal. Rule.—Double the area and extract the square root. PROBLEM 402. What is the side of a square garden whose area is 3600 sq. Solution. (1) 3600 sq. ft. = area of the garden. (2) V3600=60 ft., side of the garden.
A complete and practical solution book for the common school teacher . are of the diagonal of a square is equal totwice the square of one side, or twice the square itself. MENSURATION. 203 PROBLEM area of a square is 800 sq. ft.: what is the diagonal? Solution. (1) 800 sq. ft. = area of the square. (2) 800x2 = 1600 sq. ft., double the area. (3) v 1600 = 40 ft., the diagonal. Rule.—Double the area and extract the square root. PROBLEM 402. What is the side of a square garden whose area is 3600 sq. Solution. (1) 3600 sq. ft. = area of the garden. (2) V3600=60 ft., side of the garden. .*. 60 ft. = the side of the garden. PROBLEM 403. What is the area of a square whose diagonal is 10 Solution. (1) 10 ft. = the diagonal = AC. (2) 10X10 = 100 sq. ft. (3) 100 sq. = 50 sq. ft., the area of the square. Rule.—Divide the square of the diagonal by 2, the quotient will bethe area. PROBLEM 404. The square of half a line is equal to \ the square of the whole line. Solution. (1) = AB. s (2) AP=^=| (3) AB*=.v*, APa = -^. .. AP*=] of s*.. FIG. 84. PROBLEM 405. If the square ABCD has 40 acres in it, find the distance from C toa point & the distance from B to A, as F. 204 FAIRCHILDS SOLUTION BOOK. (1)(2)(3)(4) acres, or 6400 sq. = V6400=80 rd. FB iof 80rd. = 16rd. Now, as FCB is a right-angled tri angle, FC= VCB2+FB2 = V802+162=+ CF=81f5+ rd. PROBLEM 406.
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