1. The area of a rectangular playground is 300 sq m. If the breadth of the field is 15 m, find the length of the field.
(a) 20 m
(b) 11 m
(c) 25 m
(d) 10 m
Sol.(a)
Length = Area/breadth=300/15=20 m
2. The ratio of length and breadth of a rectangle is 5: 3. If length is 8 m more than breadth, find the area of the rectangle.
(a) 300 sq m
(b) 250 sq m
(c) 240 sq m
(d) 185 sq m
Sol.(c)
Let length =5x
Breadth =3x
5x-3x=8
2x=8⇒x=4
So,
Area = 5x×3x=15x^2
∴ 15x^2=15×16=240 sq. m
3. The perimeter of a rectangle having area equal to 144 and sides in the ratio 4 : 9 is
(a) 52 cm
(b) 56 cm
(c) 60 cm
(d) 64 cm
Sol .(a)
Area of rectangle =l×b
144=4x×9x
x=2
So, Perimeter of rectangle =2(l+b) =2(9x+4x)
=2×13×2 =52 cm
4. The area of a rectangle lies between 40 and 45 . If one of the side is 5 cm, then its diagonal lies between
(a) 8 cm and 10 cm
(b) 9 cm and 11 cm
(c) 10 cm and 12 cm
(d) 11 cm and 13 cm
Sol. (b)
Area cannot be less than 40 cm^2
Hence, other side cannot be less than =40/5=8 cm
& area cannot be greater than 45 cm^2
Hence, other side cannot be greater than =45/5=9 cm
∴ min. value of diagonal =√(8^2+5^2 )=9.43 cm
& max. value of diagonal =√(9^2+5^2 )=10.3 cm
5. The area of a rectangular field is 15 times the sum of its length and breadth. If the length of that field is 40 m, what is the breadth of that field?
(a) 24 m
(b) 25 m
(c) 28 m
(d) 32 m
Sol.(a)
A.T.Q –
Length of rectangle = 40 m
Let breadth of rectangle = x
(40+x)15=40×x
x=24 m
6. If the length of a rectangle decreases by 5 m and breadth increases by 3 m, then its area reduces 9 sq. m. If length and breadth of this rectangle increased by 3 m and 2 m respectively, then its area increased by 67 sq. m. What is the length of rectangle?
(a) 9 m
(b) 15.6 m
(c) 17 m
(d) 18.5 m
Sol.(c)
Let length of rectangle is x and breadth is y
I condition
(x-5)(y+3)=xy-9
3x-5y=6 ………….(i)
II condition
(x+3)(y+2)=xy+67
2x+3y=61 ……………(ii)
from (i) & (ii)
So, length is 17 m
7. The area of a rectangle whose length is 5 more than twice its width is 75 sq units. What is the perimeter of the rectangle?
(a) 40 units
(b) 30 units
(c) 24 units
(d) 20 units
Sol.(a)
Let the width of rectangle =x unit
Length =(2x+5) units
A.T.Q. —
Area = x(2x+5)
75=2x^2+5x
2x^2+5x-75=0
x=5,(-15)/2
So, width = 5 units
Length =2x+5=15 units
Perimeter of the rectangle =2(15+5)=40 unit
8. If the sides of a rectangle are increased by 10% find the percentage increase in its diagonals.
(a) 20%
(b) 10%
(c) 15%
(d) 18%
Sol.(b)
Percentage increase in sides = 10 %
percentage increase in diagonals = 10%
9. Area of a rectangular field is 3584 and the length and the breadth are in the ratio 7: 2, respectively. What is the perimeter of the rectangle?
(a) 246 m
(b) 292 m
(c) 286 m
(d) 288 m
Sol.(d)
Area of rectangular = length × breadth
3584=7x×2x
x=16 m
So, perimeter =2(l+b)=2(7x+2x)
=288 m
10. The length and perimeter of a rectangle are in the ratio of 5: 18. What will be the ratio of its length and breadth?
(a) 4: 3
(b) 3: 5
(c) 5: 4
(d) 4: 7
Sol.(c)
A.T.Q—
l/2(l+b) =5/18
b=4
So, ratio of l & b is 5/4
