Question 1: Find the perimeter, area and length of diagonal of a rectangle, having:
(i)
(iii)
(ii)
Answer:
(i)
(ii)
(iii)
Question 2: The perimeter of a rectangle is and its length is . Find the breadth and the area of the rectangle.
Answer:
Question 3: The perimeter of a rectangle is and its breadth is . Find the length and the area of the rectangle.
Answer:
Question 4: The perimeter of a rectangle is and its length is . Find its breadth, area and diagonal.
Answer:
Question 5: The length of a rectangle is and one of its diagonals measures . Find the breadth, perimeter and area of the rectangle.
Answer:
Question 6: The area of a rectangle is and its length is . Find the breadth and perimeter of the rectangle.
Answer:
Question 7: The area of a rectangle is and its breadth is . Find the length and perimeter of the rectangle.
Answer:
Question 8: The sides of a rectangular park are in the ratio . If its area is , find the cost of fencing it at per meter.
Answer:
and
and
Cost of fencing
Question 9: Find the cost of carpeting a room long and broad with a carpet broad at the rate of per meter.
Answer:
Length of carpet required
Cost of Carpet
Question 10: A verandah long and broad is to be paved with tiles, each measuring by . Find the number of tiles needed.
Answer:
Area of a verandah
Area of a tile
Number of tiles required
Question 11: The length and breadth of a rectangular field are in the ratio and its perimeter is . Find the cost of reaping the field at per sq. meter.
Answer:
and
and
Area of the fiels
Cost of reaping
Question 12: A room long and wide is surrounded by a verandah wide. Calculate the cost of cementing the floor of this verandah at per sq. meter.
Answer:
Therefore area of the verandah
Cost of cementing the verandah
Question 13: A rectangular grassy plot is long and broad. It has a path wide all round it on the inside. Find the cost of leveling the path at .
Answer:
Therefore area of the path
Cost of leveling the path
Question 14: A rectangular plot of land measures by . Inside the plot, a path of uniform width is to be constructed all around. The rest of the plot is to be laid with grass. Find the total expense involved in constructing the path at and laying the grass at .
Answer:
Therefore area of the path
Cost of constructing the path
Cost of laying the grass
Question 15: A rectangular hall is long and broad. A carpet is laid inside the hall leaving all around a margin of from the walls. Find the area of the carpet and the area of the strip left uncovered. If the width of the carpet is , find its cost at the rate of per meter.
Answer:
Area of carpet
Therefore area of the strip left uncovered
Cost of laying the carpet
Question 16: A rectangular lawn by has two roads each wide running in the middle of it, one parallel to length and the other parallel to breadth. Find the cost of graveling the roads at per sq. meter.
Answer:
Area of road running parallel to the
Area of road running parallel to the
Area of the road to be graveled
Cost of graveling
Question 17: The length and breadth of a rectangular park are in the ratio . A wide path running all around the outside of the park has an area of . Find the dimensions of the park.
Answer:
and
Therefore area of the path
Hence
Question 18: Find the perimeter, area and diagonal of a square each of whose sides measure: (i) (ii) (iii)
Answer:
(i) Perimeter of square
Area of square
Diagonal of square
(ii) Perimeter of square
Area of square
Diagonal of square
(iii) Perimeter of square
Area of square
Diagonal of square
Question 19: The perimeter of a square is . Find its area and the length of its diagonal.
Answer:
Perimeter
Area of square
Diagonal of square
Question 20: The diagonal of a square is . Find its area and perimeter.
Answer:
Diagonal of square:
Perimeter
Area
Question 21: The diagonal of a square is long. Find its area and perimeter.
Answer:
Diagonal of square:
Perimeter
Area
Question 22: The area of a square field is . Find its diagonal.
Answer:
Area
Diagonal
Question 23: The area of a square is . Find its perimeter and the length of its diagonal.
Answer:
Area
Perimeter
Diagonal
Question 24: A square field has an area of . Find the cost of putting the fence round it at per meter.
Answer:
Area
Perimeter
Cost of putting a fence around the field
Question 25: The cost of ploughing a square field at per square meter is . Find the cost of fencing the field at per meter.
Answer:
Area of the field
Area
Perimeter
Cost of fencing
Question 26: Find the area of the shaded region in the adjoining figure, and .
Answer:
Area of
Question 27: Find the area of the shaded region of the adjoining figure, it being given that and distance between and .
Answer:
Area of the shaded region
Question 28: Find the area of the shaded region in the adjoining figure, it being given that is a square of side and .
Answer:
Area of the shaded region
Question 29: Find the area of the shaded region of each of the following:
Answer:
(i)
Shaded area
(ii)
Shaded area
(iii) Shaded area
(iv) Shaded area
(v) Shaded area
Give the solution of s chand circle chapter class 8 icse board.