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Q:

The diagonal of a rectangle is sqrt(41) cm. and its area is 20 sq. cm. The perimeter of the rectangle must be:

A) 9 cm	B) 18 cm
C) 20 cm	D) 41 cm

Answer & Explanation Answer: B) 18 cm

Explanation:

$l^{2} + b^{2}$ = ${(d i a g o n a l)}^{2}$ =40

Also, lb=20

${(l + b)}^{2} = l^{2} + b^{2} + 2 l b$ = 41 + 40 =81

(l + b) = 9.

Perimeter = 2(l + b) = 18 cm.

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Filed Under: Volume and Surface Area

Q:

A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:

A) 10%	B) 10.08%
C) 20%	D) 28%

Answer & Explanation Answer: D) 28%

Explanation:

Let original length = x and original breadth = y.

Decrease in area = xy -[(80/100x) * (90/100y)]

=[(xy-(18/25)xy)]

=(7/25)xy

Decrease % =[(7/25)xy * (1/xy) * 100] =28%

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Q:

The diagonal of the floor of a rectangular closet is $7 \frac{1}{2}$ feet. The shorter side of the closet is $4 \frac{1}{2}$ feet. What is the area of the closet in square feet?

A) 5 .5	B) 13.5
C) 27	D) 37

Answer & Explanation Answer: C) 27

Explanation:

Other side= $\sqrt{[{(\frac{15}{2})}^{2} - (\frac{9^{2}}{2})]} f t$ = $\sqrt{\frac{225}{4} - \frac{81}{4}} f t$ = $\sqrt{\frac{144}{4}}$ = 6ft

Area of closet =(6 x 4.5)sq.ft = 27 sq.ft

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Q:

In a 1 km race, A beats B by 28 meters in 7sec. Find A's time over the course?

A) 5min,4sec	B) 4min,3sec
C) 2min,3sec	D) 3min,4sec

Answer & Explanation Answer: B) 4min,3sec

Explanation:

B covers 28 meters in 7sec. So, B's time over the course = (7/28)*100 =250 sec.

Whereas A's time over the course = 250 -7 = 243 sec.

i.e A's time over the course is 4min , 3 sec.

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Filed Under: Races and Games

Q:

A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

A) 2.91 m	B) 3 m
C) 5.82 m	D) None of these

Answer & Explanation Answer: B) 3 m

Explanation:

Area of the park = (60 x 40) = 2400 sq.m

Area of the lawn = 2109 sq.m

Area of the crossroads = (2400 - 2109) = 291 sq.m

Let the width of the road be x metres. Then,

60x + 40x - (x * x) = 291

=>(x * x) - 100x + 291 = 0

=>(x - 97)(x - 3) = 0

=>x=3

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Q:

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) 16cm	B) 18cm
C) 24cm	D) .Data inadequate

Answer & Explanation Answer: B) 18cm

Explanation:

2(l+b)/b = 5/1

=> 2l + 2b = 5b

=> 3b = 2l

=> b =(2/3) x l

Then, Area = 216 sq.cm

l x b = 216

=> l x [(2/3)x l] =216

=> l x l = 324

=> l = 18 cm.

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Filed Under: Volume and Surface Area

Q:

An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

A) 2%	B) 2.02%
C) 4%	D) .4.04%

Answer & Explanation Answer: D) .4.04%

Explanation:

100 cm is read as 102 cm.

A1 = (100 x 100) and A2 =(102 x 102)

(A2 - A1) = [(102 x 102)-(100 x 100) ]= 404

Percentage error =[404/(100 x 100 )] x 100%= 4.04%

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Filed Under: Volume and Surface Area

Q:

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 & Explanation Answer: B) 153600

Explanation:

Perimeter = Distance covered in 8 min. = (12000/60) * 8 = 1600m

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) = 153600

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Filed Under: Volume and Surface Area

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