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### Grade 7 - Mathematics9.46 Area of Rectangular Path - III

 Example: A path of uniform width runs around and outside a square plot of side 20 metres. If the area of the path is 276 square metres find its width. Solution: Let the width of the path be x metres. Now each side of the given square plot = 20 metres. Therefore, each side of the outer square = (20 + 2x) metres, because the path runs outside. The are of the path = (The area of outer square) - (The area of the inner square) = (20 + 2x)2 - 202 But the area of the path is given to be 276 square metres. Therefore, (20 + 2x)2 - 202 = 276 (20 + 2x)2 = 202 + 276 (20 + 2x)2 = 400 + 276 (20 + 2x)2 = 676 Take square roots on both sides Ö(20 + 2x)2 = Ö676 20 + 2x = 26 2x = 26 - 20 2x = 6 x = 6/3 \ The width of the path = 3 metres. Directions: Read the above example carefully and answer the following questions: Draw a square plot of side 12 centi-metres and label its sides. Draw a path of uniform width around and outside the square plot. If the area of the path is given by 256 square centi-metres, then find the width of the path. Use different colors to represent the path and the square plot.
 Q 1: A path of uniform width runs around and outside a square plot of side 25 metres. If the area of the path is 399 square metres find its width.3.5 metres2 metres2.5 metres3 metres Q 2: A path of uniform width 4 metres runs around and outside a square plot. If the area of the path is 288 square metres find a side of the square plot.45 metres5 metres15 metres14 metres Q 3: A path of uniform width 2 metres runs around and outside a square plot of side 22 metres. find the area of the path.100 square metres192 square metres205 square metres105 square metres Q 4: A path of uniform width runs around and outside a square plot of side 18 metres. If the area of the path is 517 square metres find its width.4 metres5.5 metres4.5 metres5 metres Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only!