Q 23 A rectangular grassy lawn measuring 48 m by 35 m is to be surrounded externally by a path, which is 2.5 m wide. Find the cost of the leveling the path at the rate of 4.50 per sq m.
Marks (5)
Q 24 A rectangle and a square have the same perimeter 100 m. find the side of the square. If the rectangle has a breadth 2 m less than that of the square, find, breadth, length and area of the rectangle.
Marks (5)
Q 25 Two cross roads each 3 m wide, run at the right angle through the centre of a rectangular park 72 m by 50 m, such that each is parallel to one of the side of the rectangle. Find the area of the remaining portion of the park also find the cost of gravelling these path at Rs. 4.50 per sq m.
Marks (
Q 23.)Perimeter of the grassy lawn = 2 (48 + 35 ) = 166 m.
Length of the grassy lawn including path = 48 + 5 = 53
Breadth of the grassy lawn including path = 35 + 5 = 40
Perimeter of the grassy lawn including the path = 2( 53 + 40) = 186 m.
Length of the path = Perimeter of the grassy lawn including path - perimeter of the grassy lawn
= 186 m. - 166 m. = 20 m.
Perimeter of the path = 2(20 + 2.5) = 45m
cost of fencing the path = 45 m * 4.50 = Rs . 202.50
24.) Area of the square=100m
Area of a square=side*side
Therefore, side of the square=10m
Area of the rectangle=100m
Breadth of the rectangle= 10m-2m=8m
Therefore, length of the rectangle=100/8=12.5m
25.) Area of the rectangle=72 * 50m=3600m
Area of the path= 3600m2-(72-6*50-6)m2=696m2
Area of the remaining portion=3600-696m=2904m2
Cost of gravelling the path=696*4.50=3132 rupees