1. One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field.
A) 120m2120m2120m2
B) 130m2130m2130m2
C) 140m2140m2140m2
D) 150m2150m2150m2
Ans.A
We know h2=b2+h2=>Other side =(17)2−(15)2−−−−−−−−−−−√=289−225−−−−−−−−√=64−−√=8meterArea=Length×Breadth=15×8m2=120m2We know h2=b2+h2=>Other side =(17)2−(15)2−−−−−−−−−−−√=289−225−−−−−−−−√=64−−√=8meterArea=Length×Breadth=15×8m2=120m2We know h2=b2+h2=>Other side =(17)2−(15)2−−−−−−−−−−−√=289−225−−−−−−−−√=64−−√=8meterArea=Length×Breadth=15×8m2=120m2
2. 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) 152600m2152600m2152600m2
B) 153500m2153500m2153500m2
C) 153600m2153600m2153600m2
D) 153800m2153800m2153800m2
Ans. C
Perimeter = Distance travelled in 8 minutes,
= Perimeter = 12000/60 * 8 = 1600 meter. [because Distance = Speed * Time]
As per question length is 3x and width is 2x
We know perimeter of rectangle is 2(L+B)
So, 2(3x+2x) = 1600
= x = 160
So Length = 160*3 = 480 meter
and Width = 160*2 = 320 meter
Finally, Area = length * breadth
= 480 * 320 = 153600
3. The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
A) 32%
B) 34%
C) 42%
D) 44%
Ans. D
Let original length = x metres and original breadth = y metres.
Original area =xy m2New Length =120100x=65xNew Breadth =120100y=65y=>New Area =65x∗65y=>New Area =3625xyArea Difference=3625xy−xy=
1125xyIncrease%=DiffernceActual∗100=11xy25∗1xy∗100=
=44%Original area =xy m2
New Length =120100x=65x
New Breadth =120100y=65y
New Area =65x∗65y
New Area =3625xyArea
Difference=3625xy−xy=1125xy
Increase%=DiffernceActual∗100
=11xy25∗1xy∗100=44%
4. The area of a rectangle is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the rectangular field ?
18 meter
20 meter
22 meter
25 meter
Ans. B
Let breadth =x metres.
Then length =(115x/100)metres.
=x∗115×100=460×2
=(460×100/115)x2
=400x = 20 = x∗115×100
=460×2=(460×100/115)x2
=400x = 20 = x∗115×100 = 460×2 = (460×100/115)x2 = 400x = 20
5. 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.ft, how many feet of fencing will be required ?
A) 88 feet
B) 86 feet
C) 84 feet
D) 82 feet
Ans. A
We are given with length and area, so we can find the breadth.
as Length * Breadth = Area
=> 20 * Breadth = 680
=> Breadth = 34 feet
Area to be fenced = 2B + L = 2*34 + 20
= 88 feet
