面積計算 - 例題解析

答案 - B

解析

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.

答案 - A

解析

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.

答案 - A

解析

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.

答案 - B

解析

By pythogerous theorem Other side = √((34)2- (30)2) = 16
⇒Area = (30 x 16) m2 = 480 m2

答案 - C

解析

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.

答案 - A

解析

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

答案 - D

解析

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.

答案 - D

解析

Area of the square = 1/2 (diagonal)2= 1/2x7.22≡ 7.2x7.2/2=25.92 m2

答案 - B

解析

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.

答案 - B

解析

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.

答案 - A

解析

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.

答案 - A

解析

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%.

答案 - B

解析

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.

答案 - A

解析

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

答案 - A

解析

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.

答案 - B

解析

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.

答案 - A

解析

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

答案 - A

解析

Perimeter =2√(202+102 )  =20√5 cm

答案 - B

解析

Area is larger square =1/2 x 82 =32
⇒ Area is smaller square=32/2=16 m2

答案 - A

解析

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.