Question 1: Find the perimeter and area of a rectangle whose Length and breadth are and respectively.

Answer:

Dimensions of the rectangle: Length Breadth

Therefore Perimeter

Area

Question 2: A rectangular room floor is in area. If its length is , find its perimeter.

Answer:

Dimensions of the rectangle: Length Let Breadth

Area of rectangle

Hence Breadth

Question 3: Find the length of a Diagonal of a rectangle whose adjacent sides are and long.

Answer:

Dimensions of the rectangle: Length Let Breadth

Diagonal of a rectangle

Question 4: Find the length of a diagonal of a Square of side .

Answer:

Dimension of a square: Side

Diagonal of a square

Question 5: Find the perimeter of a square the sum of the lengths of whose diagonal is .

Answer:

Dimension of a square: Side

Given: Diagonal of the square

We know diagonal of a square

Perimeter of a square

Question 6: The length and breadth of a room are in the ratio . Its area is . Find its perimeter.

Answer:

Dimensions of the rectangle: Let Length Let Breadth

Given: Area is

Therefore

Hence Length Let Breadth

Therefore Perimeter

Question 7: The diagonal of a square is . Find the diagonal of a square whose area is twice the area of .

Answer:

Given: Diagonal of a square is

If the side of the square

… … … … … (i)

Let the side of the second square

Given:

Diagonal … … … … … (ii)

Substituting (i) in (ii) we get

Diagonal

Question 8: The perimeter of a square is . Find its diagonal.

Answer:

Perimeter

Hence Diagonal

Question 9: Find the area of a square that can be inscribed in a circle of radius .

Answer:

Radius

Hence the length of the side

Therefore Area

Question 10: Find the perimeter of a square the sum of the lengths of whose diagonals is .

Answer:

Let the side be

Given:

Therefore Perimeter

Question 11: The diagonal of a square is . Find its area.

Answer:

Let the side of the square

Given:

Therefore Area

Question 12: Find the area and perimeter of a square plot of land the length of whose diagonal is .

Answer:

Given: Diagonal

Let the side of the square

Therefore

Therefore Area

Hence the Perimeter

Question 13: Find the ratio of the area of a square to that of the square drawn on its diagonal.

Answer:

Let the side of square

Therefore diagonal

Hence the ratio

Question 14: The diagonal of square is . Find the diagonal of square whose area is half of the area of .

Answer:

Let the side of square

Therefore

Let the side of square

Therefore

Diagonal of square

Question 15: The perimeter of a square is . The area of a rectangle is less than the area of the given square. If the length of the rectangle is , find its breadth.

Answer:

Let the side of the square

Therefore

Let the breadth of the rectangle

Therefore

Question 16: The perimeter of one square is and that of another is . Find the perimeter and the diagonal of a square whose area is equal to the sum of the areas of these two squares.

Answer:

Let the side of square 1

Therefore 4

Hence the area of square 1

Let the side of square 2

Therefore 4

Hence area of square 2

Therefore area of square 3

Hence the side of square 3

Therefore the perimeter of square 3

Diagonal of square 3

Question 17: The perimeter of a rectangular card board is . If its breadth is , find the length and area of the card board.

Answer:

Dimensions of the rectangle: Length Breadth

Therefore

Hence area

Question 18: If the sides of two squares are in the ratio , prove that their areas are in the ratio .

Answer:

Side of square 1

Therefore Area of square 1

Side of square 2

Therefore Area of square 2

Therefore ratio of areas

Question 19: In exchange for a square plot one of whose sides is , a man wants to buy a rectangular plot long and of the same area as of the square plot. Find the width of the rectangular plot.

Answer:

Side of square plot

Length of rectangular plot

Let breadth of rectangular plot

Therefore

Question 20: A rectangular lawn has two roads each with wide running in the middle of it, one parallel to the length and other parallel to the breadth. Find the cost of graveling them at paisa per square meter.

Answer:

Area of graveled road

Therefore cost of graveling

Question 21: The area of a square plot is hectare. Find the diagonal of the square.

Answer:

Let the side of square plot

Therefore hectare

We know 1 hectare

Therefore

Hence diagonal

Question 22: A lawn is in the form of a rectangle having its sides in the ratio . The area of the lawn is . Find the cost of fencing it at the rate of per meter.

Answer:

Let length and breadth

Therefore

Therefore length and breadth

Therefore perimeter

Therefore cost of fencing

Question 23: The area of a square park is . Find the cost of fencing it at the rate of per meter.

Answer:

Area of square

Let side of the square

Therefore Perimeter

Therefore cost of fencing

Question 24: The area of the base of a rectangular tank is and its sides are in the ratio . Find the cost of planting flowers round it at the rate of per meter.

Answer:

Let length and breadth

Therefore

Therefore length and breadth

Therefore perimeter

Therefore cost of planting flowers

Question 25: A rectangular field meter long has got an area of , what will be the cost of fencing that field on all the four sides, if meter of fencing costs paisa?

Answer:

Length

Area

Therefore breadth

Perimeter

Therefore cost of fencing

Question 26: A rectangular grassy plot is . It has gravel path wide all around it on the inside. Find the area of the path and the cost of constructing it at the rate of per sq. meter.

Answer:

Dimensions of park: Length , Breadth

Inner Dimensions of park: Length , Breadth

Area of path

Therefore cost of construction

Question 27: There is a square field whose side is . A flowerbed is prepared in its center, leaving a gravel path of uniform width all around the flower bed. The total cost of laying the flower bed and graveling the path at and per square meter respectively is . Find the width of the gravel path.

Answer:

Let the side of the garden

Therefore the area of the garden

Area of the path

Therefore

*This post first appeared on Icse Mathematics « MATHEMATICS MADE EASY FOR STUDENTS, please read the originial post: here*