51. The greater segments of a line divided internally in extreme and mean ratio is 1 foot 6 inches; find the length of the line.

52. The projections of the legs of a right upon the hypotenuse are 27cm and 48cm; find the lengths of the legs.

53. Find the width of a street, where a ladder 95.8 feet long will reach from a certain point in the street to a window 67.3 feet high on one side, and to one 82.5 feet high on the other side. (Log.)

54. Find the diameter of a O in which the chord of half the arc subtended by a chord of 30cm is 17cm.

55. Find the altitude of an equilateral ▲ whose side= 2.2TM.

56. What is the diameter of a O when the point from which a tangent of 6 feet is drawn is 8 inches from the circumference ?

57. The sides of a are 185m, 227m, and 242m; find the three altitudes, the bisectors of the three, and the radius of the circumscribed O. (Log.)

58. The sides of a trapezoid are 437.3 feet, 91 feet, 291.7 feet, and 91 feet; find the altitude of the trapezoid and the diagonals.

59. The sides of a parallelogram are 24 miles and 311⁄2 miles, and one of the diagonals is 28 miles; find the number of kilometres in the other diagonal.

60. If a chord of 2 feet is 5 inches from the centre of a O, what is the distance of a chord whose length is 10 inches?

61. One side of a is 136cm, the altitude of the Ato the second side is 102cm, the diameter of the circumscribed O is 184cm; find the third side of the A.

62. The common chord of two intersecting

whose

radii are 2 feet 1 inch and 1 foot 9 inches is 1 foot 2 inches; find the distance between their centres.

63. Is the

whose sides are 38", 36", 12", acute, right,

or obtuse?

64. In the

whose sides are 11", 13", 14", find the segments into which the side 14 is divided by the perpendicular from the opposite vertex.

65. Find the legs of a right when their projections upon the hypotenuse are 11.16 feet and 19.84 feet.

66. The sides of a ▲ are 23 feet, 27 feet, 38 feet; find the length of the median to the longest side and its projection upon the longest side.

67. What is the longest and shortest chord that can be drawn through a point 15cm from the centre of a radius is 39cm ?

whose

68. How long is the shadow of a house 23m high, when a stake 4 feet high casts a shadow 2 feet 6 inches long? (Log.)

69. Find the length of the common tangent of two ℗ which cuts the line joining their centres, when this line is 2 feet and the radii of the are 5 inches and 3 inches.

70. The greater leg of a right is 1 inch, and the difference between the hypotenuse and the less leg is inch; find the hypotenuse, the less leg, the perpendicular from the vertex of the right to the hypotenuse, and the segments of the hypotenuse made by this perpendicular.

71. Find the product of the segments of any chord passing through a point 8m from the centre of a O whose diameter is 20m.

72. Through a point 21cm from the circumference of a is drawn a secant 84cm long. The chord part of this secant is 51cm. Find the radius of the O.

73. The diagonals A C and B D of an inscribed quadrilateral intersect at E, A C is 59m, B E 35m, and D E 18" ; find A E and C E.

74. What is the length of a tangent drawn from a point 4 inches from the circumference of a whose radius is 3 feet 9 inches ?

75. Find the diameter of a O in which two chords, 30 feet and 40 feet long, parallel and on opposite sides of the diameter, are 35 feet apart.

76. The smaller segment of a line divided externally in extreme and mean ratio is 12cm; find the length of the greater segment.

77. Two sides of a are 16Km and 9Km, and the median to the first side is 11Km; find the length of the third side in miles.

78. In the preceding problem, find the lengths of the projections of the median and the second and third side upon the first side.

79. Find the lengths of the projections of each side upon the other two sides in a whose sides are 6TM, 8TM, and 12m.

80. How far apart are two parallel chords 48 feet and 14 feet long in a whose diameter is 50 feet, if they are on the same side of the centre?

BOOK IV.

1. Find the area of a rectangle whose base and altitude are 37 feet and 14 feet.

2. What is the area of a parallelogram whose base and altitude are 13m and 18m ?

3. How many hektares in a rectangular field 53Dm by 29Dm ?

4. Find the width of a rectangular field containing an acre, if the length is 176 yards.

5. How many acres in a parallelogram whose base and altitude are 17Hm and 13Hm? (Log.)

6. How many rods in the side of a square field containing a hektare? (Log.)

7. How many metres in the side of a square field containing an acre? (Log.)

8. A rectangle which is 7 times as long as it is wide contains 32 square rods; find its width and length.

9. Find the area of the surface of a flower-bed 4.55m long and 2.75m wide.

10. The perimeter of a rectangle is 24m, and the length is 9.2m; find the breadth and the area of the rectangle.

11. What is the ratio of the areas of two rectangular fields, one of which is 231m long and 87m wide, and the other 58m wide and 110m long?

12. Two rectangles have the same altitude, and the area of the first is 62 acres and the area of the second 38 acres.

If the base of the first is 570 rods, what is the base of the second?

13. What part of a mile is the perimeter of a square hektare (1km mile)?

Km

=

14. The perimeter of a rectangle is 6 feet, and the length is 3 times the breadth; find the length, the breadth, and the area of the rectangle.

15. If the perimeter of a rectangle is 26m and its length is 2.5 more than its breadth, find its length, breadth, and

area.

16. A parallelogram whose area is one acre has a base of 60 rods; and one whose area is 1a has the same altitude; find the base of the latter. (Log.)

17. Find the side of a square equivalent in area to a rectangle whose base is 4 feet 6 inches and whose altitude is 6 inches.

18. What is the altitude of a rectangle whose base is 23m, equivalent to a square whose area is 5.06 ?

19. Find the area of a whose base and altitude are respectively 3 feet 2 inches and 5 yards 1 inch.

20. Find the base and altitude of a rectangle whose perimeter is 54m and whose area is 1829m

21. Find the side of a square whose area is 18 square yards 7 square feet.

22. Find the area, in acres, of a rectangle whose perimeter is 156Dm and whose dimensions are to each other as 67. (Log.)

23. A whose base is 35cm contains .525; how many square inches in a whose homologous base is 14cm ? (Log.)