3. The sides of a rectangular park are in the ratio 4:3. If its area is
fencing it at 30 per metre.
4. The area of a rectangular field is 3584 m2 and its length is 64 m. A boy runs around the
field at the rate of 6 km/h. How long will he take to go 5 times around it?
A verandah is 40 m long and 15 m broad. It is to be paved with stones, each measuring 6
Answers
Answer:
3. ABCD is a rectangular park
Comsider AB and BC be the sides of the rectangle AB:BC = 4:3
∴ let AB=4x and BC=3x
Area of rectangle = l×b
4x x 3x = 1728
⇒12x
2
= 1728
⇒x
2
=
2
1728
⇒x
2
=144
⇒x=
144
= 12
Hence Length = 4x = 4 x12 = 48m
Breadth = 3x = 3 x 12 = 36m
∴ Perimeter of a rectangle = 2(l+b)
⇒2(48+36) = 2 x 84 = 168m
Cost of fencing = perimeter × Rate= 168 x 2.50
The total cost of fencing is Rs.420
4. Breadth = 3584/64 = 56 Mtrs. = 5 x 2(Length + Breadth) = 5 x 2(64 + 56) = 10 x 120 = 1200 Mtrs. = 1.2 Kms. So the time the boy will take = 1.2/6 = 0.2 Hrs x 60 = 12 Mins.
5. Area of Verandah=l×b
Area of Verandah=40×15=600m
2
Area of each stone=6dm×5dm=30dm
2
=30×10
−2
m
2
Number of stone =
Areaofeachstone
AreaofVerandah
Number of Stones=
30×10
−2
600
Number of stones=2000
Given area of field = 3584m
2
length = 64 m
We know area - length × breadth = l×b
b=
64
3584
=56m
Now Perimeter of field = 2[l+b]
=2[64+56]
Perimeters of field = 2[120]= 240 m.
for 5 rounds perimeter = 240×5=1200m
Given speed of boy = 6 km/h = 6×
18
5
=
3
5
m/sec
then time taken to cover 1200 m distance =
5
1200
×3
Time = 240×3sec
or Time =
60
240×3
min=12min
∴ 12 min required to complete 5 rounds of field.
