Area, General Mathematics

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: A man cycles round the boundary of a rectangular park at the rate of 12 kmph and completes one full round in 8 minutes. If the ratio between the length and breadth of the park be 3 : 2 then its area is :
A
`1536 m^2`

B
`15360 m^2`

C
`153600 m^2`

D
None

Note: Perimeter = Distance covered in 8 min. `= ((12000)/(60) xx 8) m` `= 1600 m.` Let length = 3x metres and breadth = 2x metres. Then,` = 2 (3x + 2x)` `= 1600 or x = 160` :. Length = 480 m and breadth = 320 m :. Area` = (480 xx 320) m^2` `= 153600 m^2`
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Question: One side of a rectangle is 8 metres long and its diagonal measures 17 metres. The area of the rectangle is :
A
`126 m^2`

B
`63 m^2`

C
`144.5 m^2`

D
`120 m^2`

Note: Other side` = sqrt((17)^2 - 8^2` `= sqrt(289) - 64` `= sqrt(225)` `= 15 m.` :. Area `= (15 xx 8) m^2` `= 120 m^2`
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Question: The area of a rectangle 108 m long is the same as that of a square having each side 72 m long. The width of the rectangle is :
A
`36 m`

B
`48 m`

C
`42 m`

D
`37.5 m`

Note: Let, breadth = x metres. Then, `108 xx x = 72 xx 72 or x` `= ((72 xx 72)/(108))` `= 48 m.`
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Question: The area of a square is 0.5 hectare. Its diagonal is :
A
`50 m`

B
`100 m`

C
`250 m`

D
`50sqrt(2)`

Note: Area` = (1/2 xx 10000) m^2` `= 5000 m^2` `:. 1/2 (Diagonal)` `= 5000 or (Diagonal) m^2` `= 10000.` = Diagonal` = sqrt(10000)` `= 100 m`
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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 :

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 :

Question: A man cycles round the boundary of a rectangular park at the rate of 12 kmph and completes one full round in 8 minutes. If the ratio between the length and breadth of the park be 3 : 2 then its area is :

Question: One side of a rectangle is 8 metres long and its diagonal measures 17 metres. The area of the rectangle is :

Question: The area of a rectangle 108 m long is the same as that of a square having each side 72 m long. The width of the rectangle is :

Question: The area of a square is 0.5 hectare. Its diagonal is :