General Mathematics

Question: If the side of a square is increased by 5 cm, the area increases by 165 sq. cm. The side of the square is :
A
`13 cm`

B
`14 cm`

C
`15 cm`

D
`12 cm`

Note: Let, original side = x cm. Then, `(x + 5)^2 - x^2` `= 165 => 10x` `= 140 or x = 14.` :. Side of the square` = 14 cm.`
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Question: The length of a rectangle is doubled while its breadth is halved. What is change in area ?
A
`50% increase`

B
`75% increase`

C
`37.5% increase`

D
No change

Note: Let,length = a & breadth = b. Then, area = ab. New length = 2a & New breadth` = b/2.` :. New Area` = (2a xx b/2) = ab = original area.` Thus, there is no change in area.
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Question: A hall 36 m long and 15 m broad is to be paved with stones, each measuring 6 dm by 5 dm. The number of stones required is :
A
`180`

B
`1800`

C
`18`

D
`18000`

Note: Area of the hall` = (3600 xx 1500) sq. cm.` Area of each stone` = (60 xx 50) sq. cm.` :. Number of stones` = ((3600 xx 1500)/(60 xx 50))` ` = 1800.`
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Question: A hall 36 m long and 15 m broad is to be paved with stones, each measuring 6 dm by 5 dm. The number of stones required is :
A
`180`

B
`1800`

C
`18`

D
`18000`

Note: Area of the hall` = (3600 xx 1500) sq. cm.` Area of each stone` = (60 xx 50) sq. cm.` :. Number of stones` = ((3600 xx 1500)/(60 xx 50))` ` = 1800.`
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Question: A rectangle plot is half as long again as it is broad and its area is `2/3` hectares. Then, its length is :
A
`100 m`

B
`33.33 m`

C
`66.66 m`

D
`(100sqrt(3))/3 m`

Note: Let breadth = x. Then, length` = 3/2 x `metres. Area` = (3/2 xx 10000) sq.m.` `:. 3/2 x xx x = 2/3 xx 10000 or x^2` `= 4/9 xx 10000 or x` `= 2/3 xx 100`. :. Length `= 3/2 x (3/2 xx 2/3 xx 100) m` `= 100 m.`
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Question: The area of a rectangle is thrice that of a square. If the length of the rectangle is 40 cm and its breadth is` 3/2` times that of the side of the square, then the side of the square is :
A
`15 cm`

B
`20 cm`

C
`30 cm`

D
`60 cm`

Note: Let the side of the square be x. Then, breadth of rectangle` = 3/2 x` `:. 40 xx 3/2 x = 3x^2 or x = 20` Hence, the side of the square is 20 cm.
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Question: The area of a rectangle is thrice that of a square. If the length of the rectangle is 40 cm and its breadth is` 3/2` times that of the side of the square, then the side of the square is :
A
`15 cm`

B
`20 cm`

C
`30 cm`

D
`60 cm`

Note: Let the side of the square be x. Then, breadth of rectangle` = 3/2 x` `:. 40 xx 3/2 x = 3x^2 or x = 20` Hence, the side of the square is 20 cm.
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Question: A rectangle has 15 cm as its length and 150 sq. cm as its area. If the area is increased to `1 1/3` times the original area by increasing its length only, than the new perimeter is :
A
`50 cm`

B
`60 cm`

C
`70 cm`

D
`80 cm`

Note: Breadth` = (150)/(15) cm` `= 10 cm` New area` = (4/3 xx 150) sq.cm` `= 200 sq.cm.` :. New length` = (200)/(10) cm` `= 20 cm.` New perimeter` = 2 (20 + 10) cm = 60 cm.
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Question: A rectangle carpet has an area of 120 sq. metres and a perimeter of 46 metres. The length of its diagonal is :
A
`15 m`

B
`16 m`

C
`17 m`

D
`20 m`

Note: Let length = a metres and breadth = b metres. Then,` 2 (a + b) = 46 or a + b` = 23. also, ab = 120 :. Diagonal` = sqrt(a^2 + b^2)` `= sqrt(a + b)^2 - 2ab` `= sqrt((23))^2 - 240` `= sqrt(289)` `= 17 m`
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Question: A room 5.44 m long and 3.74 m broad is to be paved with square tiles. The least number of square tiles required to cover the floor is :
A
176

B
192

C
184

D
162

Note: Area of the room`= (544 xx 374)` sq. cm. Size of largest square tile = H.C.F. of 544 cm & 374 cm `= 34 cm` Area of 1 tile` = (34 xx 34)` sq. cm. :. Number of tiles` = ((544 xx 374)/(34 xx 34))` `= 176`
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Question: If the side of a square is increased by 5 cm, the area increases by 165 sq. cm. The side of the square is :

Question: The length of a rectangle is doubled while its breadth is halved. What is change in area ?

Question: A hall 36 m long and 15 m broad is to be paved with stones, each measuring 6 dm by 5 dm. The number of stones required is :

Question: A hall 36 m long and 15 m broad is to be paved with stones, each measuring 6 dm by 5 dm. The number of stones required is :

Question: A rectangle plot is half as long again as it is broad and its area is `2/3` hectares. Then, its length is :

Question: The area of a rectangle is thrice that of a square. If the length of the rectangle is 40 cm and its breadth is` 3/2` times that of the side of the square, then the side of the square is :

Question: The area of a rectangle is thrice that of a square. If the length of the rectangle is 40 cm and its breadth is` 3/2` times that of the side of the square, then the side of the square is :

Question: A rectangle has 15 cm as its length and 150 sq. cm as its area. If the area is increased to `1 1/3` times the original area by increasing its length only, than the new perimeter is :

Question: A rectangle carpet has an area of 120 sq. metres and a perimeter of 46 metres. The length of its diagonal is :

Question: A room 5.44 m long and 3.74 m broad is to be paved with square tiles. The least number of square tiles required to cover the floor is :