Question

A rectangle has twice the area of a square. the rectangle is 18 inch by 4 inch . what is the perimeter of the square

Answer 1

`\bf \textit{area of a rectangle}\\\\ A_r=lw\quad \begin{cases} l=length\\ w=width\\ -----\\ l=18\\ w=4 \end{cases}\implies A_r=18\cdot 4\implies A_r=72\\\\ -------------------------------\\\\`


`\bf \textit{area of a square}\\\\ A_s=lw\quad \textit{area of a rectangle}\\\\ A_r=lw\quad \begin{cases} l=length\\ w=width\\ l=w=x \end{cases}\implies A_s=x\cdot x\implies A_s=x^2\\\\ -------------------------------\\\\ A_r=2\cdot A_s\implies 72=2x^2\implies\cfrac{72}{2}=x^2\implies 36=x^2 \\\\\\ √(36)=x\implies \boxed{6=x}`

the square has 4 sides, thus its perimeter is 6+6+6+6.

Answer 2

Rectangle:

A = BH
= (18)(4)
= 72

Finding area of square:

72 = 2x
/2 /2
36 = x

Finding perimeter of square using area:

P = √a * 4
= √36 * 4
= 6 * 4
= 24

Therefore the perimeter of the square is 24 inches. I am not sure so sorry for any mistakes.