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What are the dimensions of a square lawn that is surrounded by a walk 1m wide and the area of the walk is equal to half the area of the lawn?
ColeD
The dimensions of the lawn are about 8.9m x 8.9m. Solved using the steps below: Since the lawn is a square we'll let one side be x, therefore the area of the lawn is x2 The area of the walkway is the area of the walkway plus the lawn minus the area of the lawn. Since the lawn is surrounded by a 1m wide walkway each side of the walkway & lawn is x+1m+1m or x+2, so the area of the walkway & lawn together is (x+2)*(x+2). {Draw a picture to help you} Now the area of the walkway as mentioned above is the area of the walkway & lawn minus the area of the just the lawn, so we have (x-2)2 - x2 In the problem you stated that the area of the walk is half the area of the lawn. so we have: (x-2)2 - x2 = (1/2)*x2 Using algebra we have a quadratic equation simplified to: x2-8x-8=0 Using the quadratic formula, we solve for x. One solution is negative so we can discard that for this problem. The other solution is approximately 8.899m. Use the value of x and check your answer.
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