Question

Hola me puedes ayudar por favor

Answer 1

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,

`\begin{gathered} \text{Area of square= Side length}*\text{Side length} \\ =x* x \\ =x^2 \end{gathered}`

The expression to calculate the area of the rectangle is,

`\begin{gathered} \text{Area of the rectangle=Lenght}* Width \\ =(x+4)*(x-2) \\ =x^2-2x+4x-8 \\ =x^2+2x-8 \end{gathered}`

Given the area of the square ane the rectangle are same.

`\begin{gathered} \text{Area of square= Area of rectangle} \\ x^2=x^2+2x-8 \\ x^2-x^2=2x-8 \\ 0+8=2x \\ (8)/(2)=x \\ 4=x \\ x=4 \end{gathered}`

The lenght of th square is x=4

Substitute x=4 in the expresso=ion to calculate the length of the rectangl.

`\begin{gathered} Length=x+4 \\ =4+4 \\ =8 \end{gathered}`

Thus, the lenght of the rectangular rug is 8.