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 11 in. What is the area of the outer part of the rug?
Added by Juan Carlos G.
Step 1
Since the width of the outer region is 11 inches, the side length of the outer square is the side length of the inner square plus twice the width of the outer region. Therefore, the side length of the outer square is \( x + 2 \times 11 = x + 22 \) inches. Show more…
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Write the indicated formula. Then, using x as the variable, complete the steps below: The area of the rug is 85 sq units. Find its length and width. Write an equation. To write an equation, use the formula obtained above and substitute 85 = (x + 6)(x - 6) (Do not simplify: Type an equation) Use the distributive property: 85 = x^2 - 36 Simplify. 121 = x^2 Add 36 to both sides. (Simplify your answer.) Apply the square root property to the equation obtained above and solve for x: x = 11, -11 (Simplify your answer: Use a comma to separate answers as needed.) The length of the rectangular rug is x + 6 = 17 units The width of the rectangular rug is x - 6 = Enter your answer in the answer box and then click Check Answer
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