Respuesta :
Given Data:
The given side length of a square is: x
The length of the rectangle is 4 yadr grater than the square. Thus, the length of the rectangle is: x+4
The width of the rectangle is 2 yard less than the square. Thus, the width of the rectangle is: x-2.
The expression to calculate the area of the square is,
[tex]\begin{gathered} \text{Area of square= Side length}\times\text{Side length} \\ =x\times x \\ =x^2 \end{gathered}[/tex]The expression to calculate the area of the rectangle is,
[tex]\begin{gathered} \text{Area of the rectangle=Lenght}\times Width \\ =(x+4)\times(x-2) \\ =x^2-2x+4x-8 \\ =x^2+2x-8 \end{gathered}[/tex]Given the area of the square ane the rectangle are same.
[tex]\begin{gathered} \text{Area of square= Area of rectangle} \\ x^2=x^2+2x-8 \\ x^2-x^2=2x-8 \\ 0+8=2x \\ \frac{8}{2}=x \\ 4=x \\ x=4 \end{gathered}[/tex]The lenght of th square is x=4
Substitute x=4 in the expresso=ion to calculate the length of the rectangl.
[tex]\begin{gathered} Length=x+4 \\ =4+4 \\ =8 \end{gathered}[/tex]Thus, the lenght of the rectangular rug is 8.
