Area

Question:
The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

[A].

16 cm

[B].

18 cm

[C].

24 cm

[D].

Data inadequate

Answer: Option B

Explanation:

2(l + b)	=	5
b		1

2l + 2b = 5b

3b = 2l

b =	2	l
	3

Then, Area = 216 cm2

l x b = 216

l x	2	l	= 216
	3

l2 = 324

l = 18 cm.

Question:
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?

[A].

34

[B].

40

[C].

68

[D].

88

Answer: Option D

Explanation:

We have: l = 20 ft and lb = 680 sq. ft.

So, b = 34 ft.

Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft.

Question:
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

[A].

15360

[B].

153600

[C].

30720

[D].

307200

Answer: Option B

Explanation:

Perimeter = Distance covered in 8 min. =		12000	x 8	m = 1600 m.
		60

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 x 320) m2 = 153600 m2.

Question:
The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?

[A].

40

[B].

50

[C].

120

[D].

Data inadequate

Answer: Option E

Explanation:

Let breadth = x metres.

Then, length = (x + 20) metres.

Perimeter =		5300		m = 200 m.
		26.50

2[(x + 20) + x] = 200

2x + 20 = 100

2x = 80

x = 40.

Hence, length = x + 20 = 60 m.

Question:
The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

[A].

1520 m2

[B].

2420 m2

[C].

2480 m2

[D].

2520 m2

Answer: Option D

Explanation:

We have: (l – b) = 23 and 2(l + b) = 206 or (l + b) = 103.

Solving the two equations, we get: l = 63 and b = 40.

Area = (l x b) = (63 x 40) m2 = 2520 m2.