E. Equations of the form x2+ ax + bc = 0. NOTE. As regards maxima and minima, see note under D. 116. To divide a given line into two parts, so that their product shall be equal to the area of a given rectangle. 117. Given Cin AB; to find a point X in AB between B and C, so that AX2 = BX × CX. 118. Given C'in AB; to find a point X in AB between A and C, so that AB: AX= BX: CX. 119. To construct a rectangle equivalent to a given rectangle, and having a perimeter equal to that of another given rectangle. 120. To construct a right triangle, given a+b, c. 121. To construct a right triangle, given a—b, c. 122. To divide the greater side of a given rectangle into two parts, so that the sum of their squares shall be equal to the area of the rectangle. 123. To transform a given square into an isosceles triangle in which the sum of the base and the altitude is given. 124. In a given square to inscribe another square the side of which has a given length. 125. To transform a given triangle into a rectangle having the same perimeter. ANSWERS TO THE NUMERICAL EXERCISES IN CHAPTERS III., IV., V. 25. 3, 4, 5. The second solution (-1, 0, +1) does not belong to this question. 26. 24, 32. 27. 33, 44, 55. 28. 12 ft. 29. 2.238, 3.059. 30. 8 in. and 2 in. 31. r√3, 120°. 32. 12 in. 33. √+2. 34. √200 14.142 in. = = 35. Each tangent = 8 in.; chord of contact ; r = a, and ab is a diameter. 37. Obtuse, since 82+92<132. (No. 163.) 5. 220 yds. 7. $60.48. 8. $166.50. 9. 7.789 yds. 10. 49 sq. ft. 54 sq. in. 11. 7 acres 3920 sq. yds. 12. 8748 sq. yds. 13. 11 yds. 14. 97 yds. 21 ft. 15. 288 sq. ft. 16. 25 sq. ft. 17. 225 sq. yds. 22. 42 ft. and 18 ft. 23. 16 ft. and 12 ft. 24. 2700qm. 25. 60 ft. and 40 ft. 26. 4 ft. 27. 7168 tiles. 28. 2 ft. 4 in. 29. $558.32. 30. Gained $3518. 31. No difference. 32. 11,250 sq. ft. 33. 96qm. 34. 108 sq. ft. |