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A square purple rug has a orange square in the center. The side length of the orange square is x inches. The width of the purple band that surrounds the orange square is 10 in. What is the area of the purple ​band?

Respuesta :

Answer:

[tex]40(x+10)$ square inches[/tex]

Step-by-step explanation:

  • Side length of the Orange Square =x inches

Width of the purple band that surrounds the orange square = 10 in.

Since the orange square is in the middle

From the diagram:

  • Side Length of the Purple Rug =(x+20) Inches

Therefore:

Area of the Purple Band =Area of Purple Rug -Area of Orange Square

[tex]=(x+20)^2-x^2\\[/tex]

[tex]=(x+20)(x+20)-x^2\\=x^2+20x+20x+400-x^2\\=40x+400\\=40(x+10)$ square inches[/tex]

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