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1.	An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
Answer» 100 cm is read as 102 cm. A1 = (100 x 100) cm2 and A2 (102 x 102) cm2. (A2 - A1) = [(102)2 - (100)2] = (102 + 100) x (102 - 100) = 404 cm2. Percentage error = 404 x 100 % = 4.04% 100 x 100

2.	A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:
Answer» Let original length = x and original breadth = y. Decrease in area = xy - 80 x x 90 y 100 100 = xy - 18 xy 25 = 7 xy. 25 Decrease % = 7 xy x 1 x 100 % = 28%. 25 xy

3.	The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:
Answer» We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103. Solving the two equations, we get: l = 63 and b = 40. Area = (l x b) = (63 x 40) m2 = 2520 m2.

4.	The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?
Answer» Let original length = x and original breadth = y. Original area = xy. New length = x . 2 New breadth = 3y. New area = x x 3y = 3 xy. 2 2 Increase % = 1 xy x 1 x 100 % = 50%. 2 xy

5.	The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?
Answer» Let breadth = x metres. Then, length = (x + 20) metres. Perimeter = 5300 m = 200 m. 26.50 2[(x + 20) + x] = 200 2x + 20 = 100 2x = 80 x = 40. Hence, length = x + 20 = 60 m.

6.	A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
Answer» We have: l = 20 ft and lb = 680 sq. ft. So, b = 34 ft. Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft.

7.	A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:
Answer» Area to be plastered = [2(l + b) x h] + (l x b) = {[2(25 + 12) x 6] + (25 x 12)} m2 = (444 + 300) m2 = 744 m2. Cost of plastering = Rs. 744 x 75 = Rs. 558. 100

8.	The diagonal of the floor of a rectangular closet is 7 feet. The shorter side of the closet is 4 feet. What is the area of the closet in square feet?
Answer» Other side = 15 2 - 9 2 2 2 ft = 225 - 81 4 4 ft = 144 4 ft = 6 ft. Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.

9.	A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?
Answer» Let the side of the square(ABCD) be x metres. Then, AB + BC = 2x metres. AC = 2x = (1.41x) m. Saving on 2x metres = (0.59x) m. Saving % = 0.59x x 100 % = 30% (approx.) 2x

10.	The diagonal of a rectangle is cm and its area is 20 sq. cm. The perimeter of the rectangle must be:
Answer» l2 + b2 = 41. Also, lb = 20. (l + b)2 = (l2 + b2) + 2lb = 41 + 40 = 81 (l + b) = 9. Perimeter = 2(l + b) = 18 cm.

11.	What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
Answer» Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. Area of each tile = (41 x 41) cm2. Required number of tiles = 1517 x 902 = 814. 41 x 41

12.	The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
Answer» Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m2.

13.	The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
Answer» Let original length = x metres and original breadth = y metres. Original area = (xy) m2. New length = 120 x m = 6 x m. 100 5 New breadth = 120 y m = 6 y m. 100 5 New Area = 6 x x 6 y m2 = 36 xy m2. 5 5 25 The difference between the original area = xy and new-area 36/25 xy is = (36/25)xy - xy = xy(36/25 - 1) = xy(11/25) or (11/25)xy Increase % = 11 xy x 1 x 100 % = 44%. 25 xy Video Explanation: https://youtu.be/I3jLjLPn1W4

14.	The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
Answer» 2(l + b) = 5 b 1 2l + 2b = 5b 3b = 2l b = 2 l 3 Then, Area = 216 cm2 l x b = 216 l x 2 l = 216 3 l2 = 324 l = 18 cm.

15.	A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
Answer» Area of the park = (60 x 40) m2 = 2400 m2. Area of the lawn = 2109 m2. Area of the crossroads = (2400 - 2109) m2 = 291 m2. Let the width of the road be x metres. Then, 60x + 40x - x2 = 291 x2 - 100x + 291 = 0 (x - 97)(x - 3) = 0 x = 3. Video Explanation: https://youtu.be/R3CtrAKGxkc