- 1. The sides of a rectangle are in the ratio 4:3 and its area is 972sq.m find the perimeter of rectangle

A.120m

B.122m

C.124m

D.126m

Answer & Explanation

Answer: Option D

Explanation:**let 4x and 3x be sides of the rectangle**

We know that area of rectangle = l×b

4x × 3x = 972

12x2 = 972

X2 = 81

X = 9

Therefore length = 4x = 4×9 = 36m

Breadth = 3x = 3×9 = 27m

Therefore perimeter = 2 (l+b) = 2(36+27) = 126m

We know that area of rectangle = l×b

4x × 3x = 972

12x2 = 972

X2 = 81

X = 9

Therefore length = 4x = 4×9 = 36m

Breadth = 3x = 3×9 = 27m

Therefore perimeter = 2 (l+b) = 2(36+27) = 126m

- 2. Find the cost of carpenting a room 13m long and 9m broad with a carpet 75cm broad at the rate of Rs.20 per metre

A.Rs.3100

B.Rs.3120

C.Rs.3080

D.Rs.3112

Answer & Explanation

Answer: Option B

Explanation:**Area of the carpet = area of the room**

= 13×9=117sq.m

Breadth of the carpet = 75cm = 3/4m

Length of the carpet = area/breadth (A=L×B=>L=A/B)

=117×4/3=156m

Hence, cost of carpet = 156×20 =Rs.3120

= 13×9=117sq.m

Breadth of the carpet = 75cm = 3/4m

Length of the carpet = area/breadth (A=L×B=>L=A/B)

=117×4/3=156m

Hence, cost of carpet = 156×20 =Rs.3120

- 3. The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle.

A.10 cm

B.15 cm

C.20 cm

D.18 cm

Answer & Explanation

Answer: Option C

Explanation:**Let breadth = x. Then, length =**

Length of the rectangle = 20 cm.

*2x.*Then,*(2x*- 5) (x + 5) - 2x * x = 75 => 5x - 25 = 75 => x = 20.Length of the rectangle = 20 cm.

- 4. If each side of a square is increased by 25%, find the percentage change in its area.

A.62.25

B.59.52

C.58.75

D.56.25

Answer & Explanation

Answer: Option D

Explanation:**Let each side of the square be**

New side =(125a/100) =(5a/4). New area = (5a/4)

Increase in area = ((25

Increase% = [((9a

*Then, area =*^{a. }*a*^{2}*.*New side =(125a/100) =(5a/4). New area = (5a/4)

^{2}=(25a^{2})/16.Increase in area = ((25

*a*^{2}*)/16)*-a^{2}=(9a^{2})/16.Increase% = [((9a

^{2})/16)×(1/a^{2})×100] % = 56.25%.- 5. A man walking at the rate of 6km per hour crosses a square field diagonally in 9 seconds the area of the field is

A.110sq.m

B.111.5aq.m

C.112.5sq.m

D.114sq.m

Answer & Explanation

Answer: Option C

Explanation:**Distance covered in 9 seconds = (6×1000/3600)×9 = 15m**

Diagonal of square field = 15m

Side of square =a then diagonal of that square= √2 a

Hence area of the square = a

Diagonal of square field = 15m

Side of square =a then diagonal of that square= √2 a

Hence area of the square = a

^{2}= (15^{2})/2 =112.5 sq.m**To whom this Area Questions and Answers section is beneficial?**

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