Area, General Mathematics

Question: If the base of a rectangle is increased by `10%` and the area is unchanged then the corresponding altitude must be decreased by :
A
`10%`

B
`9 1/11%`

C
`11%`

D
`11 1/9%`

Note: Let, length = a & breadth = b. Then, area = ab. New length` = (110)/(100) a = (11a)/10.` Let new breadth = c. Then,` (11a)/10 xx c = ab or c = (10b)/11.` :. Decrease in breadth` = (b/11 xx 1/b xx 100)%` `= 9 1/11%`
1. Report
Question: If the base of a rectangle is increased by `10%` and the area is unchanged then the corresponding altitude must be decreased by :
A
`10%`

B
`9 1/11%`

C
`11%`

D
`11 1/9%`

Note: Let, length = a & breadth = b. Then, area = ab. New length` = (110)/(100) a = (11a)/10.` Let new breadth = c. Then,` (11a)/10 xx c = ab or c = (10b)/11.` :. Decrease in breadth` = (b/11 xx 1/b xx 100)%` `= 9 1/11%`
1. Report
Question: If the base of a rectangle is increased by `10%` and the area is unchanged then the corresponding altitude must be decreased by :
A
`10%`

B
`9 1/11%`

C
`11%`

D
`11 1/9%`

Note: Let, length = a & breadth = b. Then, area = ab. New length` = (110)/(100) a = (11a)/10.` Let new breadth = c. Then,` (11a)/10 xx c = ab or c = (10b)/11.` :. Decrease in breadth` = (b/11 xx 1/b xx 100)%` `= 9 1/11%`
1. Report
Question: A rectangle carpet has an area of 60 sq.m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is :
A
`5 m`

B
`12 m`

C
`13 m`

D
``14.5 m`

Note: Let, length = x metres and breadth = y metres. Then, xy = 60 and `sqrt(x^2 + y^2 + x = xy` :. xy = 60 and` (x^2 + y^2) = (5y - x^2)` or xy = 60 and` 24y^2 - 10xy = 0` `:. 24y^2 - 10 xx 60 = 0 or y^2` `= 25 or y = 5` `:. x = (60/5) m` = 12 m. So, length of the carpet = 12 m.
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Question: The number of square shared tin sheets of side 20 cm that can be cut off from a square tin sheet of side 1 metre, is :
A
5

B
10

C
25

D
20

Note: Number of sheets `= ((100 xx 100)/(20 xx 20))` `= 25`
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Question: The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by :
A
`35%`

B
`42%`

C
`62%`

D
`82%`

Note: Let side of the square be a. Then, area` = a^2`. New length` = ((140)/(100) a)` `= (7a)/5,` New breadth` = ((130)/(100) a)` `= (13a)/10.` New area` = (7a)/5 xx (13a)/10` `= (91a^2)/50` Increase in area` = (41/50 a^2 xx 1/a^2 xx 100)%` `= 82%`
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Question: The cost of papering the four walls of a room is Rs.475. Each one of the length, breadth and height of another room is double that of this room. The cost of papering the walls of this new room is :
A
Rs. 950

B
Rs. 1425

C
Rs. 1900

D
Rs. 712.50

Note: Let the dimensions of former room be x,y and z. Then, the area of its 4 walls` = 2 (x +y) xx z sq.` units. :. Area of 4 walls of this room `= 2 (2x + 2y) xx 2z` `= 4 xx [2 (x + y) xx z]` `= 4 xx (Area of 4 walls of 1st room)` :. Required cost `= Rs. (475 xx 4)` `= 1900`
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Question: If the area of a rhombus is 15 sq. cm and the length of one of its diagonals is 5 cm, then the length of the other diagonal is :
A
3 cm

B
5 cm

C
6 cm

D
7 cm

Note: Area` = 1/2 xx `(product of diagonals) `:. 1/2 xx 5 xx x = 15 => x = (15 xx 2/5)` `= 6 cm`
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Question: If one side and one diagonal of a rhombus are 5 cm and 8 cm respectively, then its area is :
A
`20 cm^2`

B
`24 cm^2`

C
`40 cm^2`

D
`26 cm^2`

Note: Halves of diagonals & side of a rhombus from a right angled triangle with side as hypotenuse. Let another diagonal = 2x. Then, `x^2 + (8/2)^2 = 5^2 or x^2` `= (5^2 - 4^2)` `= 9 or x = 3.` :. Another diagonal = 6 cm. :. Area` = (1/2 xx 8 6) sq.cm = 24 sq. cm.`
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Question: In rhombus whose area is 144 sq. cm, one of its diagonal is twice as long as the other. The lengths of its diagonal are :
A
`12 cm, 24 cm`

B
`6 cm, 12 cm`

C
`24 cm, 48 cm`

D
`18 cm, 32 cm`

Note: Let the diagonals be x and 2x cm. Then,` 1/2 (x xx 2x) = 144 or x = 12.` :. Diagonal are 12 cm and 24 cm.
1. Report

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Question: If the base of a rectangle is increased by `10%` and the area is unchanged then the corresponding altitude must be decreased by :

Question: If the base of a rectangle is increased by `10%` and the area is unchanged then the corresponding altitude must be decreased by :

Question: If the base of a rectangle is increased by `10%` and the area is unchanged then the corresponding altitude must be decreased by :

Question: A rectangle carpet has an area of 60 sq.m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is :

Question: The number of square shared tin sheets of side 20 cm that can be cut off from a square tin sheet of side 1 metre, is :

Question: The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by :

Question: The cost of papering the four walls of a room is Rs.475. Each one of the length, breadth and height of another room is double that of this room. The cost of papering the walls of this new room is :

Question: If the area of a rhombus is 15 sq. cm and the length of one of its diagonals is 5 cm, then the length of the other diagonal is :

Question: If one side and one diagonal of a rhombus are 5 cm and 8 cm respectively, then its area is :

Question: In rhombus whose area is 144 sq. cm, one of its diagonal is twice as long as the other. The lengths of its diagonal are :