Question

5. The ratio of the length of a square to the length of a rectangle is 1:3.
If length of the rectangle is 45 cm. Find the perimeter of the square.​

Answer 1

Using Formula

* perimeter of square= 4 x (Side)

* perimeter of rectangle = 2 × ( Length +

width)

Now Let,

• Length of rectangle = L • Side of square = S

A/C to question,

The ratio of the length of a square to the length of a rectangle is 1:3

==> S: L= 1:3

==> S/L = 1/3

==> 3S-L = 0 ---(1)

But, L = 45 cm

==> 3S - 45 = 0

==> 3S = 45

==>S = 45/3

==>S=15

Now, Calculate perimeter of Square

==> perimeter of Square = (Side)²

==> perimeter of Square = 15²

==> perimeter of Square = 225 cm

Hence

Side of Square- 15cm

Side of perimeter-225cm

Answer 2

$\sf{Using~Formula}$

$\sf{Perimeter~of~Square~=~4~×~(Side)}$

$\sf{Perimeter~of~Rectangle~=~2~×~(Length~+~width)}$

$\sf{Now~Let,}$

$\sf{Length~of~Rectangle~=~L}$

$\sf{Side~of~Square~=~S}$

$\sf{The~ratio~of~the~length~of~a~square}$

$\sf{to~the~length~of~a~rectangle~is~1~:~3}$

$\sf\huge{~S:~L~=~1~:~3}$

$\sf\huge\frac{S}{L}={1}{3}$

$\sf\huge{3S~- ~L~ = ~0 ~~(1)}$

$\sf{But,~L~=~45~cm}$

$\sf\huge{3S~-~45~=~0}$

$\sf\huge{3S~=~45~}$

$\sf\huge{S=\frac{45}{3}}$

$\sf\huge{S~=~15}$

$\sf{Now,~Calculate~Perimeter~of~Square}$

$\sf{Perimeter~of~Square~=~(Side)^2}$

$\sf{Perimeter~of~Square ~=~15 ^ 2}$

$\sf{Perimeter~of~Square~=~225cm}$