Answer - B
Explanation
We have: (l - b) = 33 and 2(l + b) = 134 or (l + b) = 67.
Solving the two equations, we get: l = 50 and b = 17.
∴ Area = (l x b) = (50 x 17) m2 =850 m2.
Q 2 - The length of a rectangular plot is 40 meters more than its breadth. If the cost of fencing the plot at 53 per meter is Rs. 10,600, what is the length of the plot in meters?
A - 100 m
B - 80 m
C - 60 m
D - 55 m
Answer - A
Explanation
Let breadth = X meters. Then, length = (X+ 40) meters.
Perimeter = 10600/53 =200 m
∴ 2[(X + 40) + X] = 200 2X + 40 = 100 2X = 120
⇒X = 60.
Hence, length = x + 40 = 100 m.
Answer - A
Explanation
l2 + b2 = (√(63 ))2=63 Also, lb = 37/2.
(l + b)2 = (l2 + b2) + 2lb = 63 + 37 = 100
⇒ (l + b) = 10.
∴ Perimeter = 2(l + b) = 20 cm.
Answer - B
Explanation
By pythogerous theorem Other side = √((34)2- (30)2) = 16
⇒Area = (30 x 16) m2 = 480 m2
Answer - C
Explanation
Let length = X and breadth = Y. Then,
2 (X + Y) = 92 OR X + Y = 46 AND X2 + Y2 = (34)2 = 1156.
Now, (X + Y)2 = (46)2
⇔ (X2 + Y2) + 2XY = 2116 ⇔ 1156 + 2XY = 2116
⇒ XY=480
∴ Area = XY = 480 cm2.
Q 6 - The length of a rectangle is thrice its breadth. If its length is decreased by 9 cm and breadth is increased by 9 cm, the area of the rectangle is increased by 81 sq. cm. Find the length of the rectangle.
A - 9 cm
B - 15 cm
C - 18 cm
D - 27 cm
Answer - A
Explanation
Let breadth = X. Then, length = 3X.
Then, (3X - 9) (X + 9) = 3X * X + 81
⇒3X2+27X-9X-81=3X2+81
18X=162
⇒X=9 cm
∴ Length of the rectangle = 9 cm
Q 7 - The ratio between the length and the breadth of a rectangular park is 2: 1. If a man cycling
along the boundary of the park at the speed of 18 km/hr completes one round in 10 minutes,
then the area of the park (in sq. m) is:
A - 5000 m2
B - 50 m2
C - 50000 m2
D - 500000 m2
Answer - D
Explanation
Perimeter = Distance covered in 10 min. =18000/60 x 10=3000 m
Let length = 4X meters and breadth = X meters.
Then, 2(2X +1X) = 3000 or X = 500.
Length = 1000 m and Breadth = 500 m.
∴ Area = (1000 x 500) m2 = 500000 m2.
Answer - D
Explanation
Area of the square = 1/2 (diagonal)2= 1/2x7.22≡ 7.2x7.2/2=25.92 m2
Answer - B
Explanation
Let the diagonals of the squares be 3X and 7X respectively.
Ratio of their areas = (1/2)*(3X)2 :( 1/2)*(7X)2 = 9X2: 49X2 = 9: 49.
Q 10 - The perimeters of two squares are 80 cm and 64 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.
A - 24 cm
B - 48 cm
C - 64 cm
D - 16 cm
Answer - B
Explanation
Side of first square = (80/4) = 20 cm;
Side of second square = (64/4)cm = 16 cm.
Area of third square = [(20)2 - (16)2] cm2
= (400 - 256) cm2 = 144 cm2.
Side of third square = √144 cm = 12 cm.
Required perimeter = (12 x 4) cm = 48 cm.
Q 11 - What is the least number of squares tiles required to pave the floor of a room 30 m 34 cm
long and 18 m 4 cm broad?
A - 814
B - 816
C - 800
D - 712
Answer - A
Explanation
Length of largest tile = H.C.F. of 3034 cm and 1804 cm = 82 cm.
Area of each tile = (82 x 82) cm2.
Required number of tiles 3034x1804/82x82 = 37x22=814.
Answer - A
Explanation
Let each side of the square be X. Then, area = X2.
New side =(116X/100) =(29X/25). New area = (29X/25)2
Increase in area = (29X/25)2 - X2 =841/625X2 - X2=216/625X2
⇒ Increase% = [(216/625X2x1/(X2))*100] % = 34.56%.
Answer - B
Explanation
Distance covered in one revolution = ((44 X 2000)/1000) = 88m.
⇒ 2πR = 88
⇒ 2 x (22/7) x R = 88
∴ R = 88 x (7/44) = 14 m.
Answer - A
Explanation
Let other diagonal = 2x cm.
Since diagonals of a rhombus bisect each other at right angles,
we have: (10)2 = (6)2 + (x)2
⇒ x = √((10)2 - (6)2)= √64= 8 cm.
So, other diagonal = 16 cm.
∴ Area of rhombus = (1/2) x (Product of diagonals)
= ((1/2) x 12 x 16) cm2 = 96 cm2
Answer - A
Explanation
Area = (6.7914 x 10000) m2= 67914 m2.
πR2= 67914
⇒(R)2 = (67914 x (7/22)) ⇔ R = 147 m.
Circumference = 2 π R = (2 x (22/7) x 147) m = 924 m.
Cost of fencing = Rs. (9240 x 2.20) = Rs. 20328.
Answer - B
Explanation
Let the two parallel sides of the trapezium be X cm and Y cm.
Then,X - Y = 8
And, (1/2) x (X+ Y) x 38 = 950
⇒ (X +Y) = ((950 x 2)/38)
⇒ X + Y = 50
Solving (i) and (ii), we get: X = 29, Y = 21.
So, the two parallel sides are 29 cm and 21 cm.
Answer - A
Explanation
Area of a parallelogram, A = bh
(where b is the base and h is the height of the parallelogram)
⇒ (X2 - 48) = (X-6) (X + 3)
⇒ X=10
⇒ Actual Area = 102-48=52 units
Answer - A
Explanation
Perimeter =2√(202+102 ) =20√5 cm
Q 19 - If two squares are similar but not equal and the diagonal of larger square is 8 m. What is the area of smaller square if it area is 1/2 of larger square.
A - 4 m2
B - 16 m2
C - 24 m2
D - 32 m2
Answer - B
Explanation
Area is larger square =1/2 x 82 =32
⇒ Area is smaller square=32/2=16 m2
Answer - A
Explanation
We know the area of diagonals is 1/2 x (product of diagonals)
Let the other diagonal be X
So 300 = 1/2 x X x 20
⇒ X=30 cm.
