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A square rug has an inner square in the center. The side length of the inner square is x inches, and the width of the outer region is 3 in. What is the area of the outer part of the​ rug?

A square rug has an inner square in the center The side length of the inner square is x inches and the width of the outer region is 3 in What is the area of the class=

Respuesta :

Medunno13

Answer:

[tex]12x+36[/tex] in²

Step-by-step explanation:

The area of the inner square is [tex]x^2[/tex] in².

The area of the whole square is [tex](x+6)^2[/tex] in².

Taking the difference, [tex](x+6)^2-x^2=(6)(2x+6)=12x+36[/tex] in².

ujalakhan18

Answer:

[tex]\huge\boxed{\sf 12x + 36 \ in.^2}[/tex]

Step-by-step explanation:

Formula:

  • Area of square = length²

Area of inner part of the rug:

Length = x in.

So,

Area = (x)²

Area = x² in.²

Area of the whole rug:

Length of the whole rug = 3 + x + 3 = x + 6

So,

Area = (x + 6)²

Area = x² + 12x + 36 in.²

Area of the outer part of the rug:

= Area of the whole rug - Area of the inner part

= x² + 12x + 36 - x²

= x² - x² + 12x + 36

= 12x + 36 in.²

[tex]\rule[225]{225}{2}[/tex]