Note 4.-With regard to finding the number of tiles or planks necessary for tiling or flooring a rectangular room or court, see Note 3, Prob. 2. Find the area of the outer rectangle ABCD, and also of the inner rectangle EFGH. Then, the difference of these two is the area of the walk or border. Observe that AD=EH+2 width of walk; Note 6.-To ascertain the number of yards of carpet, of a certain width, that will be required for a floor.—Find the area of the floor, and divide it by the width of the carpet. (Observe that the area of the floor and the width of the carpet must be both expressed in the same denomination, either yards, feet, or inches; and the required length of the carpet will be in the same denomination.) Note 7.-Given the length and breadth of a rectangle, to find the length and breadth (proportional to the former) of another rect H Ꮐ Supposing AB and AD of the rectangle ABCD are given, and it is required to find EF and EH (proportional to AB and AD) of another rectangle EFGH, whose area shall be twice that of the rectangle ABCD, we have— EF × EH=2(AB × AD)=AB √2 × AD√√2 (since √2 × √2=2); that is, EF, the length of required rectangle length of given rectangle x√2; and EH, the breadth of the required rectangle=breadth of given rectangle × √2. Hence, if the area is to be doubled, then the length and breadth of the required rectangle will be found by multiplying the length and breadth of the given rectangle each by √2. If the area is to be trebled, then multiply each of the given dimensions by 3; and so on. Example 1.-Find the area of a rectangular room which is 13 ft. 4 in. long and 12 ft. 8 in. broad. Area of room=13 ft. 4 in. x 12 ft. 8 in.=160 in. x 152 in. =24320 sq. in.=168 sq. ft. 128 sq. in Example 2.-Find the expense of carpeting a room which measures 18 ft. by 15 ft., with carpet 27 in. wide, worth 5s. 4d. per yd. Area of the floor=18 ft. x 15 ft.=270 sq. ft.=30 sq. yds; and 27 in. yd. Then, yards of carpet-30+3=30x=40 yds. And 40 yds., at 5s. 4d. per yard,=£10 13s. 4d. Example 3.-If it requires 1000 tiles, 8 in. long and 3 in. wide, for paving the floor of a room which is 14 ft. 7 in. long, find the breadth of the room. Each tile contains (8 × 31), or 28 sq. inches; and therefore 1000 tiles will contain 28000 sq. in., which is the area of the floor. Then, if we divide 28000 sq. in. by 14 ft. 7 in.—that is, by 175 in.-we shall have 160 in., or 13 ft. 4 in., the breadth of the floor. Example 4.-How many square feet are there in a gravel walk, 2 ft. wide, running all round the outside of a rectangular grass-plot which is 40 ft. long and 28 ft. broad? Now the extreme length of the rectangle ABCD (see fig. Note 5), which includes the grass plot and the walk= 40 ft.+4 ft.=44 ft. And the extreme breadth=28 ft.+4 ft.=32 ft. Then, the area of the larger rectangle ABCD=44 ft.× 32 ft. 1408 sq. ft.; = 1120 sq. And area of grass-plot EFGH=40ft. x 28 ft. length breadth. ft. I. Area = Find the area of the rectangle whose length and breadth are, respectively (1) Length 37 in. and breadth 27 in. (2) Length 4 yds. and breadth 3 yds. 2 ft. (3) Length 10 ft. 7 in. and breadth 9 ft. 5 in. Find the area of the rectangle whose length and breadth are, respectively— (4) Length 7 ft. 6 in. and breadth 6 ft. 7 in. (5) Length 17ft. 10 in. and breadth 51⁄2 in. (6) Length 4 yds. 2 ft. 6 in. and breadth 2 yds. 1 ft. 4 in. Determine the area of the following rectangular fields, whose dimensions are (7) 210 yds. by 180 yds. (8) 5 ch. 20 lks. by 4 ch. 35 lks. (9) 20 poles 5 yds. by 12 poles 1 yd. Find the area of the rectangle whose length and diagonal are, respectively (10) Diagonal 135 yds. and length 108 yds. (11) Diagonal 295 yds. and length 236 yds. (12) Diagonal 8.29 ft. and length 6.29 ft. Find the breadth of the rectangle when its area and length are, respectively (13) Area 155 sq. yds. 5 sq. ft. and length 13 yds. 1 ft. (14) Area 180 sq. yds. 4 sq. ft. and length 18 yds. 2 ft. (15) Area 24 sq. yds. 1 sq. ft. 80 sq. in. and length 4 yds. 2 ft. 10 in. Find the breadth of the rectangular field whose area and length are, respectively (16) Area 31 acres and length 140 yds. (17) Area 3 ac. 2 roods 10 poles 294 sq. yds. and length 136 yds. (18) Area 3 ac. 34 poles and length 12 ch. 85 lks. (19) Area 5 ac. and length 14 mile. (20) The length of a rectangular field is 6 ch. 75 lks. and its breadth 3 ch. 15 lks.; find the rental, at £2 10s. per acre. (21**) A path 8 ft. wide, surrounding a rectangular court 60 ft. long and 36 ft. wide, is to be paved with tiles 9 in. long and 4 in. wide; how many will be required? (22) A certain street, of a mile long, covers 1 acre; what is the breadth of the street? (23) The middle part of a room, which measures 20 ft. 6 in. by 16 ft., is covered with a carpet, which is only 15 ft. 9 in. long and 10 ft. 8 in. wide; how much additional carpet, 27 in. wide, will be required to cover the remaining part of the floor? (24) What will be the expense of building a wall round a rectangular garden which covers exactly acre, and whose breadth is 30 yds., at 15s. 6d. per yd.? (25) What will be the expense of making a footpath, 2 ft. wide, round the outside of a rectangular plot containing 572 sq. yds., and whose length is 26 yds., at 1s. 3d. per sq. yd. ? (26) A square piece of wood is 2 ft. 6 in. long; what must be the breadth of a rectangular piece 3 ft. 9 in. long, that it may be as large as the square piece? (27) What will be the expense of paving a hall, 50 yds. long and 50 ft. wide, with marble slabs 1 ft. long and 9 in. broad, the price of the slabs being £5 per dozen. (28*) A room 39 ft. long requires 36 yds. of carpet, 2 ft. 2 in. wide, to cover it; what is the breadth of the room? (29) The area of a rectangular field is 5 ac. 1 rood 6 poles 8 sq. yds., and its length is 256 yds.; find the expense of fencing it, at 1s. per yd. Supposing the field were a square and of the same area, what would be the expense in that case ? (30*) A rectangular field contains 3 acres, and is 100 yds. wide; find its length. (31) A rectangular field is 7 chains in length, and its area is 54 acres; what is its breadth ? (32) A rectangle, whose length is four times that of its breadth, and a square have the same perimeter, 100 yds.; which contains the greater area, and by how much? (33**) A rectangular garden is to be cut off from a rectangular field, so as to contain a quarter of an acre. One side of the field is taken for a side of the plot, and measures 3 chains; find the length of the other side. (34) The rental of a rectangular field, whose length is 1 fur. 20 poles, at the rate of £1 13s. per acre, is £6 6s.; find its breadth. (35) What will be the expense of paving a courtyard which measures 35 ft. 10 in. by 18 ft. 6 in., at 6s. 3d. per sq. yd. ? (36) Find the expense of lining the sides and bottom of a rectangular cistern, 12 ft. 9 in. long, 8 ft. 3 in. broad, and |