Find the hypothenuse of a right-angled triangle whose base is 41 feet, and perpendicular 53 feet. Ans. 67 ft., nearly. Find the cost of walling in a piece of ground in the form of a right-angled triangle whose base is 792 feet, and perpendicular 1175 feet, at 10d. per yard. Ans. £47. side. II. Given the hypothenuse and one side, to find the other Multiply their sum by their difference and extract the square root. Ex. I. The hypothenuse of a right-angled triangle is 557, and the base 165; find the perpendicular. 557 +165=722 1444 6498 2166 283024 (532 Ans. 25 103) 330 309 1062) 2124 2124 Ex. 2. The hypothenuse of a right-angled triangle is 32 ft. 5 in., and the perpendicular 15 ft. 9 in.; find the base. I. Find the base of a right-angled triangle whose perpendicular is 105, and hypothenuse 137. Ans. 88. 2. Find the perimeter of a right-angled triangle whose base is 731, and hypothenuse 1069. Ans. 2580. 3. Find the perpendicular of a right-angled triangle whose base is 8 ft. 4 in., and hypothenuse 52 ft. 5 in. Ans. 51 ft. 9 in. 4. The hypothenuse of a right-angled triangle is 505 feet, and the base 217 feet; find the expense of fencing at Ans. £15. 10s. 10d. 9žd. per yard. 5. The hypothenuse of a right-angled trianglé is 12 ft. 5 in., and the perpendicular 6 ft. 3 in.; find the base. Ans. 10.8.8 feet. 6. The hypothenuse of a right-angled triangle is 481 feet, and the base 360 feet; find the expense of fencing it round at 10d. per yard. Ans. £16. 18s. 4d. * ** As a further exercise on the two preceding rules, the student may verify any of the results in Table I. THE SQUARE. III. To find the area of a square. (1) Square the side. (2) Square the diagonal, and divide by 2. Ex. I. The side of a square field is 264 yards; find its value at £65 per acre. Ex. 2. II in. Find the area of a square whose side is 7 ft. Find the area of a square whose diagonal is 9 Ex. 3. chains 57 links. 957 957 6699 4785 8613 2 915849 4 579245 4 2 316980 40 12 67920 Ans. 4 a. 2 r. 12 p. I. 2. yards. 3. EXAMPLES. Find the area of a square whose side is 14 ft. 6 in. Find the area of a square field whose side is 396 Find the expense of boarding a square floor whose side is 16 ft. 9 in., at 41d. per yard. Ans. 11s. 8d. 4. Find the rent of a square field whose diagonal is 7 chns. 15 lks., at 45 shillings per acre. Ans. £5. 15s. old. 5. The area of a square field is 208.5.0.6 square feet; find the diagonal. Ans. 20 ft. 5 in. 6. The cost of carpeting a square floor at 3s. 6d. per square yard, amounted to £9. 35. 11d.; find the side of the square. Ans. 7 yards. THE RECTANGLE. IV. To find the area of a rectangle. Multiply the length by the breadth. Note. The area divided by the length gives the breadth; and the area divided by the breadth gives the length. Ex. 1. Find the cost of carpeting a rectangular floor whose length is 19 ft. 6 in., and breadth 12 ft. 3 in., at 3s. 6d. per square yard. |