Question

Two squares of 9cm are attached together.Find the perimeter of the resulting figure.

Answer 1

Hint: Let us take two squares of same dimension ,each of which has a side length of 9 cm.Join two squares from one of their sides.Then ,find out the summation of all outer side length of the resulting figure.This summation will be the perimeter of the resulting figure.

Formula used: Perimeter of rectangle = $2 \times \left( {{\text{length + breadth}}} \right)$

Complete step-by-step answer:
 Let us take a square ABCD of side length 9 cm.

Now, we will take another Square of the same dimension i.e 9cm. Then, we will join these two identical squares.

After joining the two squares, the resulting figure will look as given below:

As, the perimeter is the sum of outer side length. So, we will remove the inner middle side length and then, draw the final resulting figure.
Thus, the resulting figure is shown as below:

So, we can observe from the above diagram that the resulting figure is a rectangle, which is formed by joining two squares.
Thus, the resultant figure is a rectangle CDEF.
Length of rectangle CDEF =FE= (9+9) cm=18 cm ………(i)
Breadth of rectangle CDEF = DE = 9 cm…………………….(ii)
Thus, the perimeter of the resulting figure is determined by the following formula:
Perimeter of Rectangle CDEF= $2 \times ({\text{length + breadth)}}$
Putting the values of length and breadth from (i) and (ii), we get
Perimeter of Rectangle CDEF= $2 \times (18 + 9)$
Perimeter of Rectangle CDEF= $2 \times 27 = 54$cm

Thus, the required perimeter of resulting figure = Perimeter of Rectangle CDEF =54 cm.

Note: A square is a 2-dimensional figure with four sides equal and every angle is a right angle $\left( {{{90}^ \circ }} \right)$.
Perimeter of Square = $4 \times {\text{a}}$, where ‘a’ is the size length of square.
A rectangle is also a 2-dimensional figure with opposite sides equal and every angle is also a right angle$\left( {{{90}^ \circ }} \right)$.
Perimeter of Rectangle=$2 \times \left( {{\text{length}} \times {\text{breadth}}} \right)$.