Area Problems
The cost of cultivating a square field at the rate of Rs. 160 per hectare is Rs. 1440. the cost of putting a fence around it at 75 paisa per meter is?
Area = 1440 / 160 hectares = 9 hectares = 90000 m2? One side = ?90000 m = 300 mSo perimeter = 4 x 300 m = 1200 m ? Cost of fencing = Rs (1200 x 75) / 100= Rs. 900
Given that, area = 40 sq cm, base = 28 cm and height = perpendicular = ?Area = (base x perpendicular) / 2 ? 40 = (28 x perpendicular) / 2 ? perpendicular = 40/14 = 20/7 = 26/7 cm
Circular piece is 4 x 11 = 44 cm long, Then Circumference of circle is given by, 44 = pi x D, where D is the diameter D = 44 / pi Take pi = 22 / 7, then D = 44 / (22/7) = (44 x 7) / 22 D = 14 cm.
Given that, l = 2b [Here l = length and b = breadth]Decrease in length = Half of the 10 cm = 10/2 = 5 cmIncrease in breadth = Half of the 10 cm = 10/2 = 5 cm Increase in the area = (70 + 5) = 75 sq cm According to the question, (l - 5) (b + 5) = lb + 75 ? (2b - 5) (b + 5) = 2b2 + 75 [since l = 2b]? 5b - 25 = 75 ? 5b = 100? b = 100/ 5 = 20? l = 2b = 2 x 20 = 40 cm
Given that, a = 8 cm, b = 10 cm and c = 12 cm We know, that s = (a + b + c)/2 = (8 + 10 + 12)/2= 30/2 = 15 cm ? (s - a) = (15 - 8) = 7 cm (s - b) = (15 - 10) = 5 cm (s - c) = (15 - 12) = 3 cm ? Area = ?s(s - a) (s - b) (s - c)= ?15 x 7 x 5 x 3= ?1575= ?25 x 63= 5?63 cm
According to the question,l/[2(l + b)] = 5/18? 10l + 10b = 18l = 10b? l/b = 10/8 = 5/4? l : b = 5 : 4Hence, ratio of length and breadth of a rectangle is 5 : 4
EXAMIANS