aptitude : : area and perimeter
 
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Important Formulas
  Exercise
   Exercise 2
   Exercise 1
1.
The perimeter of a right-angled ∆ is 60 cm its hypotenuse is 26cm. The area of the ∆ is
 
A.
120 cm2

B.

240 cm2
C.
390 cm2
D.
780 cm2
   
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Answer: B
Explanation :
Let base= b cm   Height= h cm 
b + h+26   =60 :. b + h=34  
(b + h)2= (34)2
b2 + h= (26)2
(b + h)-( b2 + h) = (34) - (26)2
2 bh = (34+26)(34-26) = 480
   bh = 240
 1/2 bh =120
  Area = 120cm2
   






 
2.
The sides of a triangle are 3 cm, 4cm and 5cm. The area (in cm2) of the triangle formed by joining the mid­ points of sides of this triangle is
 
A.
3/4

B.

3/2
C.
3
D.
6
   
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Answer: B
Explanation :
a=3cm,b=4cm,andc=5cm
It is a right angle ∆ with base = 3 cm
h = 4cm
Area  of required ∆ = (1/4)x6= 3/2cm2
 






 
3.
If the  length  of a rectangle  is  increased  by  20%,  then
by how much percent its breadth must be decreased so
as to keep 'its area unaltered?
 
 
A.
25 %

B.

81/3 %
C.
16 2/3 %
D.
20%
   
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Answer: C
Explanation :
23. Suppose the length and the breadth of the rectangle are
x and y respectively. In the first case :
Area  of the rectangle  = xy
In the second case :
On  reducing  the  breadth  by  A%  and  increasing  the
length  by  20%
Length of the new rectangle = x + 20% of x = 1.2x
Breadth of the new rectangle = y- A% of y = y (1- A/100)
:. Area of the new rectangle = 1.2x X y (1- A/100)
According to question :
Area of the rectangle s in the two cases remain s unaltered
 xy = 1.2 xy(1- A/100) => = 1.2(100-A)/100
100 = 1.2(100- A) => 1.2A = 120-100
         A = 20/1.2 = 16 2/3
Hence, breadth of the rectangle , if decreased by 16 2/3%
area of the rectangle remains unaltered






 
4.
The base of a triangle is l5cm and height is l2cm. the height of another triangle of double the area having the base 20 cm is
 
A.
8 cm

B.

9 cm
C.
12.5 cm
D.
18 cm
   
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Answer: D
Explanation :
A1 = ( 1/2 x 15 x 12 ) = 90 cm2
A =  2A1= 180 cm2
1/2 x 20 x h = 180
therefore   h = 18 cm






 
5.
If the ratio of areas of two squares is 225 : 256,then the ratio of their perimeter is
 
A.
225:256

B.

256:225
C.
15:16
D.
16:15
   
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Answer: C
Explanation :
 a2/ b2= 225/256 =(15/16)2
 a/b =15/16
:. 4a/4b  = ( 4 x 15)/ (4 x 16) = 15/16
:. Ratio of perimeters= 15 : 16
 






 
6.
The areas of two concentric circles, forming a ring, are 154 sq.cm and 616 sq.cm. respectively. The width of the ring  is
 
A.
6 cm

B.

7 cm
C.
9 cm
D.
11 cm
   
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Answer: B
Explanation :
Suppose radius of the bigger circle = R cm
And radius of the smaller circle = r cm 
Width of the ring = (R - r) cm
:. Area of the bigger circle = π R2sq. cm
Area of the smaller circle = π r2sq . cm.
According to question :
 π R= 616 and   π r= 154
π R= 616 = > R =  616 x7/22 =>  R=  196 => R = 14
 π r= 154 = > r =  154x7/22 =>   r= 49    =>  r = 7
Width of the ring = 14- 7 = 7 cm






 
7.
If the  difference  between  the  circumference  and  the radius of a circle is 37 cm, find its diameter.
 
A.
11 cm

B.

12 cm
C.
16 cm
D.
14 cm
   
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Answer: D
Explanation :
Suppose radiu s of the circle = R cm
So Circumference of the circle = 2πR cm. 
According to question :
              2πR - R = 37
            R(2 x 22/7 -1) = 37
            R(44 - 7) = 37 x 7 => R x 37 = 37 X 7 
                    R = 37 x 7/37 = 7
        :. Radius of the circle = 7 cm
Hence diameter of the circle = 2R = 2 x 7 =  14 cm.
 
 






 
8.
If the perimeter of an equilateral triangle is 72 cm, its area will be
 
 
 
A.
144√3 sq. cm

B.

142√3 sq. cm
C.
154√2 sq. cm
D.

144√2 sq. cm

   
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Answer: A
Explanation :
Suppose  side of  the equilateral  triangle  = x cm
so Perimeter of the triangle = 3x cm 
According to question 
        3x = 72 => x = 72/3 =24 cm
Area of the equilateral triangle
             = √3/4 x  x2  
             =  √3/4 x (24)2  
             =  144√3






 
9.
If area of a square is equal to the area of a rectangle 6.4 m long and 2.5 m wide, then each side of this square measures
 
A.
8 m

B.

5.4 m
C.
3.8 m
D.
4 m
   
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Answer: D
Explanation :
Area of the rectangle   = 6.4 x 2.5 =  16.00 sq. m.
According to question :
Area of the square = Area of the rectangle 
Area of the square = 16 sq. m.
Side of  the square = √l6 = 4 m.






 
10.
The perimeter of a square is 48 cm. the area of a rectangle is 4  cm2 less than the area of the square if the length of the rectangle is 14cm then its perimeter is
 
A.
24cm

B.

48cm
C.
50cm
D.
54cm.
   
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Answer: B
Explanation :
Side of the square = 12cm
Area ofthe rectangle   = (12 x 12 - 4)cm2= 140cm2
Breadth  =area/length = 140/14 = 10cm
Perimeter= 2 x (l + b)= 2 x (14 + 10) = 48 cm






 

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