Selina solutions concise mathematica class 7 icse Solutions for Chapter 20 mensuration

Q1) The length and the breadth of a rectangular plot are 135 m and 65 m. Find, its perimeter and the cost of fencing it at the rate of ₹60 per m.

Q2) The length and breadth of a rectangular field are in the ratio 7 : 4. If its perimeter is 440 m, find its length and breadth. Also, find the cost of fencing it @ ₹150 per m.

Q3) The length of a rectangular field is 30 m and its diagonal is 34 m. Find the breadth of the field and its perimeter.

Q4) The diagonal of a square is 12\sqrt{2}cm Find its perimeter.

Q5) Find the perimeter of a rectangle whose length = 22.5 m and breadth = 16 cm.

Q6) Find the perimeter of a rectangle whose length = 22.5 m and breadth = 16 dm.Find the perimeter of a rectangle with length = 24 cm and diagonal = 25 cm

Q7)The length and breadth of a rectangular piece of land are in the ratio of 5 : 3. If the total cost of fencing it at the rate of ₹48 per metre is ₹19,200, find its length and breadth.

Q8) A wire is in the shape of square of side 20 cm. If the wire is bent into a rectangle of length 24 cm, find its breadth.

Q9) If P = perimeter of a rectangle, l= its length and b = its breadth find :

(i) P, if l = 38 cm and b = 27 cm

(ii) b, if P = 88 cm and l = 24 cm

(iii) l, if P = 96 m and b = 28 m

Q10) The cost of fencing a square field at the rate of Cost of fencing 440 m = ₹150 x 440 = ₹75 per meter is Cost of fencing 440 m = ₹150 x 440 = ₹67,500. Find the perimeter and the side of the square field.

Q11) The length and the breadth of a rectangle are 36 cm and 28 cm. If its perimeter is equal to the perimeter of a square, find the side of the square.

Q12) The radius of a circle is 21 cm. Find the circumference.

Q13) The circumference of a circle is 440 cm. Find its radius and diameter.

Q14) The diameter of a circular field is 56 m. Find its circumference and cost of fencing it at the rate of ₹80 per m.

Q15) The radii of two circles are 20 cm and 13 cm. Find the difference between their circumferences.

Q16) The diameter of a circle is 42 cm, find its perimeter. If the perimeter of the circle is doubled, what will be the radius of the new circle.

Q17) The perimeter of a square and the circumference of a circle are equal. If the length of each side of the square is 22 cm, find:

(i) perimeter of the square.

ii) circumference of the circle.

(iii) radius of the circle.

Q18) Find the radius of the circle whose circumference is equal to the sum of the circumferences of the circles having radii 15 cm and 8 cm.

Q19) Find the diameter of a circle whose circumference is equal to the sum of circumference of circles with radii 10 cm, 12 cm, and 18 cm.

Q20) The circumference of a circle is eigth time the circumference of the circle with radius 12 cm. Find its diameter.

Q21) The radii of two circles are in the ratio 3 : 5, find the ratio between their circumferences.

Q22) The circumferences of two circles are in the ratio 5 : 7, find the ratio between their radii.

Q23) The perimeters of two squares are in the ratio 8:15, find the ratio between the lengths of their sides.

Q24) The lengths of the sides of two squares are in the ratio 8:15, find the ratio between their perimeters. Solution:

Q25)Each side of a square is 44 cm. Find its perimeter. If this perimeter is equal to the circumference of a circle, find the radius of the circle.

Q1) Find the area of a rectangle whose length and breadth are 25 cm and 16 cm.

Q2) The diagonal of a rectangular board is 1 m and its length is 96 cm. Find the area of the board.

Q3) The sides of a rectangular park are in the ratio 4 : 3. If its area is 1728 m.sq, find (i) its perimeter (ii) cost of fencing it at the rate of ₹40 per meter.

Q4) A floor is 40 m long and 15 m broad. It is covered with tiles, each measuring 60 cm by 50 cm. Find the number of tiles required to cover the floor.

Q5) The length and breadth of a rectangular piece of land are in the ratio 5 : 3. If the total cost of fencing it at the rate of ₹24 per meter is ₹9600, find its : (i) length and breadth (ii) area (iii) cost of leveling at the rate of ₹60 per m.sq

Q6) Find the area of the square whose perimeter is 56 cm.

Q7) A square lawn is surrounded by a path 2.5 m wide. If the area of the path is 165 m^2 find the area of the lawn.

Q8) For each figure, given below, find the area of shaded region : (All measurements are in cm)

Q9) One side of a parallelogram is 20 cm and its distance from the opposite side is 16 cm. Find the area of the parallelogram.

Q10) The base of a parallelogram is thrice it height. If its area is 768 cm^2 , find the base and the height of the parallelogram.

Q11) Find the area of the rhombus, if its diagonals are 30 cm and 24 cm.

Q12) If the area of a rhombus is 112 cm^2 and one of its diagonals is 14 cm, find its other diagonal.

Q13) One side of a parallelogram is 18 cm and its area is 153 cm ^2 . Find the distance of the given side from its opposite side.

Q14) The adjacent sides of a parallelogram are 15 cm and 10 cm. If the distance between the longer sides is 6 cm, find the distance between the shorter sides.

Q15) The area of a rhombus is 84 cm^2 and its perimeter is 56 cm. Find its height.

Q16) Find the area of a triangle whose base is 30 cm and height is 18 cm.

Q17) Find the height of a triangle whose base is 18 cm and area is 270 cm^2 .

Q18)The area of a right-angled triangle is 160 cm^2 . If its one leg is 16 cm long, find the length of the other leg.

Q31) A circular racing track has inner circumference 528 m and outer circumference 616 m. Find the width of the track.

Q32) The inner circumference of a circular track is 264 m and the width of the track is 7 m. Find: (i) the radius of the inner track. (ii) the radius of the outer circumference. (iii) the length of the outer circumference. (iv) the cost of fencing the outer circumference at the rate of ₹50 per m.

Q33) The diameter of every wheel of a car is 63 cm. How much distance will the car move during 2000 revolutions of its wheel.

Q34) The diameter of the wheel of a car is 70 cm. How many revolutions will it make to travel one kilometre?

Q35) A metal wire, when bent in the form of a square of largest area, encloses an area of 484 cm^2 . Find the length of the wire. If the same wire is bent to a largest circle, find:

(i) radius of the circle formed.

(ii) area of the circle.

Q36) A wire is along the boundary of a circle with radius 28 cm. If the same wire is bent in the form of a square, find the area of the square formed.

Q37) The length and the breadth of a rectangular paper are 35 cm and 22 cm. Find the area of the largest circle which can be cut out of this paper.

Q38) From each comer of a rectangular paper (30 cm x 20 cm) a quadrant of a circle of radius 7 cm is cut. Find the area of the remaining paper i.e., shaded portion.