Question

two squares of area 16cm square and 36cm square are placed adjacent to each other to form a new shape the perimeter ​

Answer 1

Answer:

$\red\bigstar$Perimeter of The New Shape = 32cm.

SOLUTION

Let us Assume that the First Square is ABCD.

Let us Assume that the second Square is PQRS.

GIVEN :-

Area of First Square ABCD = 16cm².

Area of Second Square PQRS = 36cm².

SQUARE ABCD

Area of a Square = a²( a is the side)

$\implies$ 16 = a²

$\implies$ a = √16 = 4

★ Side (a) of the First Square ABCD = 4cm.

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf D}\put(-0.5,4.2){\bf A}\put(4.2,-0.5){\bf C}\put(4.2,4.2){\bf B}\put(1.5,-0.6){\bf\large \ cm}\put(4.4,2){\bf\large 4\ cm}\end{picture}$

SQUARE PQRS

Area of a Square = a²( a is the side)

$\implies$ 36 = a²

$\implies$ a = √36 = 6

★ Side (a) of the second square PQRS = 6cm.

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf R}\put(-0.5,4.2){\bf P}\put(4.2,-0.5){\bf S}\put(4.2,4.2){\bf Q}\put(1.5,-0.6){\bf\large 6\ cm}\put(4.4,2){\bf\large 6\ cm}\end{picture}$

Perimeter of the new figure formed on placing these two squares adjacent to each other = Perimeter of Square ABCD - 4cm + Perimeter of Square PQRS - 4cm.

Perimeter of ABCD

Perimeter of a square = 4a ( a is the side)

Here,

Side (a) = 4cm.

$\implies$ Perimeter of Square ABCD = 4 × 4 = 16cm.

Perimeter of PQRS

Perimeter of a square = 4a ( a is the side)

Here,

Side (a) = 6cm.

$\implies$ Perimeter of Square PQRS = 4 × 6 = 24cm.

Perimeter of The New Shape = 16 - 4 + 24 - 4 = 12 + 20 = 32cm.

Answer 2

Given : two squares of area 16cm square and 36cm square are placed adjacent to each other to form a new shape

To Find :   the perimeter ​ of new shape

Solution:

squares of area 16cm square

=> Side of Square  =  √16  = 4 cm

Perimeter of Square = 4 * 4  = 16 cm

squares of area 36cm square

=> Side of Square  =  √36  = 6 cm

Perimeter of Square = 4 * 6  = 24 cm

Square are placed adjacent to each other to form a new shape

Side of 4 cm of Square will be touching side of square of 6 cm

Hence 4 cm will be subtracted from each perimeter

16  - 4 + 24 - 4  = 32 cm

or add perimeter as shown in figure

= 4 + 6 + 6 + 6 + 2 + 4 + 4

= 32 cm

the perimeter ​ of new shape  = 32 cm

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