1. One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field.
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:
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:
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=
=44%Original area =xy m2
New Length =120100x=65x
New Breadth =120100y=65y
New Area =65x∗65y
New Area =3625xyArea
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 ?
Let breadth =x metres.
Then length =(115x/100)metres.
=400x = 20 = x∗115×100
=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
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