A rectangular sheet of paper of length 10 cm and breadth 8 cm is cut into two identical pieces along the dotted lines as shown below (figure 1). The two pieces are then joined to form a new shape (Figure 2)

?if the height and width of each step in the new shape are EQUAL, what is the Perimeter  of the new shape in Figure 2?

A. 36 cm
B. 48 cm
C. 52 cm
D. 56 cm 

Dear Student,

Please find below the solution to the asked query:

We form our diagram , As :

Given : The height and width of each step in the new shape are equal , So we assume 

Height of each step  = Width of each step =  x 

And we consider only width of each step ( As we have shown in figure 1 ) and get :

x  + x + x  + x  =  8 ,   As that sum of width of each step from figure 1 is same as breadth of rectangular sheet

4 x  = 8

x  = 2

So, Height of each step  = Width of each step = 2 cm 

Now we show height and width of each step ( As we have shown in figure 2 ) .

Then ,

Perimeter  of the new shape in Figure 2 =   8 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 8 = 48 cm

Therefore,

Option ( B )                                                                 ( Ans )


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