Question 1

If the perimeters of a square and a rectangle are the same, then the area a & b enclosed by them would satisfy the condition:

Accepted Answer

Take a square of side 4cm and a rectangle having l=6cm and b=2cm then perimeter of square = perimeter of rectangle area of square = 16 sq.cm area of rectangle = 12 sq.cm Hence a >b

Question 2

The area of a square field is 69696sq.cm..its diagonal will be equal to

Accepted Answer

d = 2 * s = > d = 2 * 69696

Question 3

A rectangular parking space is marked out by painting three of its sides.If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, then what is the area of the parking space in square feet?

Accepted Answer

Let l = 9 ft. Then l + 2b = 37 => 2b = 37 – l = 37 – 9 = 28 b = 28/2 = 14 ft. Area = lb = 9 × 14 = 126 sq. ft.

Question 4

The area of a field in the shape of a trapezium measures 1440sq m. The perpendicular distance between its parallel sides is 24cm. If the ratio of the sides is 5:3, the length of the longer parallel side is:

Accepted Answer

Area of field = 1 2 * 5 x + 3 x * 24 = 96x sq.m 96x = 1440 => x = 1440 96 = 15 Hence, the length of longer parallel side = 5x = 75m

Question 5

A rectangular paper when folded into two congruent parts had a perimeter of 34cm foer each part folded along one set of sides and the same is 38cm. When folded along the other set of sides. What is the area of the paper?

Accepted Answer

when folded along the breadth we have 2(l/2 +b) = 34 or l+2b = 34...........(1) when folded along the length, we have 2(l+b/2)=38 or 2l+b =38.....(2) from 1 &2 we get l=14 and b=10 Area of the paper = 14*10 = 140 sq cm

Question 6

The perimeter of a square is 40 meters. Find the length of one side of the square

Accepted Answer

P = 4 x s

Question 7

The perimeter of a rectangle is 160 cm. The rectangle is 4 times longer than wide. What are the length and width of this rectangle?

Accepted Answer

P=2(l+b) l=4b

Question 8

A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?

Accepted Answer

Draw the diagram. The diagonal of the rectangle is the diameter of the circle. The diagonal is the hypotenuse of a 3,4,5 triangle and is therefore, 5. Circumference = π.diameter = 5π

Question 9

A triangle has a perimeter 13. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?

Accepted Answer

The measure of the third side of a triangle must lie between the sum and the difference of the other two sides. Using this fact along with the answer choices, we can eliminate the wrong answers. Option A cannot be correct because 4 would not be the longest side.(sides 4, 5, and 4) Option B could be correct because the other two sides would be 3 and 4. Option C cannot be correct because this third side would be greater than the sum of the other two sides.

Question 10

2 metres broad pathway is to be constructed around a rectangular plot on the inside. The area of the plots is 96 sq.m. The rate of construction is Rs. 50 per square metre. Find the total cost of the construction?

Accepted Answer

Given lb =96 Area of pathway = [(l-4)(b-4)-lb] = 16-4(l+b) Which cannot be determined. so, data is inadequate.

Question 11

The edge of three cubes of metal is 3 m, 4 m and 5 m. They are melted and formed into a single cube. Find the edge of the new cube ?

Accepted Answer

The edge of the new cube is = 3 3 + 4 3 + 5 3 = a 3 => a = 6 m.

Question 12

A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ?

Accepted Answer

Length = 6 m 24 cm = 624 cm Width = 4 m 32 cm = 432 cm HCF of 624 and 432 = 48 Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117.

Question 13

Calculate the number of bricks, each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 cm x 6 m when 10% of its volume is occupied by mortar ?

Accepted Answer

Let the number of bricks be 'N' 10 x 4/100 x 6 x 90/100 = 25/100 x 15/100 x 8/100 x N 10 x 4 x 6 x 90 = 15 x 2 x N => N = 720.

Question 14

Two concentric circles form a ring. The inner and outer circumference of the ring are 352/7 m and 528/7m respectively.Find the width of the ring.

Accepted Answer

let the inner and outer radii be r and R meters then, 2 πr = 352/7 => r = (352/7) * (7/22) * (1/2) = 8m 2 πR = 528/7 => R= (528/7) * (7/22) * (1/2)= 12m width of the ring = R-r = 12-8 = 4m

Question 15

The perimeters of two squares are 40cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.

Accepted Answer

side of first square = 40/4 =10cm side of second square = 32/4 = 8cm area of third squre = 10² - 8² = 36 sq cm side of third square = 36 = 6 cm required perimeter = 6*4 = 24cm

Question 16

A cow s tethered in the middle of a field with a 14feet long rope.If the cow grazes 100 sq feet per day, then approximately what time will be taken by the cow to graze the whole field?

Accepted Answer

area of the field grazed = (22/7) * 14 * 14 = 616 sq feet

Question 17

Wheels of diameters 7cm and 14cm start rolling simultaneously from x & y which are 1980 cm apart towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after 10seconds.The speed o…

Accepted Answer

let each wheel make x revolutions per sec. Then 2 π * 7 2 * x + 2 π * 7 * x * 10 = 1980 2 * 22 7 * 7 2 * x + 2 * 22 7 * 7 2 * x = 198 66 x = 198 distance moved by smaller wheel in 3 revolutions = 2 * 22 7 * 7 2 * 3 = 66 c m speed of smaller wheel = 66 3 m/s = 22m/s

Question 18

The length of the rectangle is 20% more than its breadth . what will be the ratio of the area of the rectangle to that of the square whose side is equal to the breadth of the rectangle?

Accepted Answer

Required ratio = 6 x 5 × x × 1 x 2 = 6 : 5

Area Questions