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Question

A park square in shape has a $$3$$ metre wide road inside it running along its sides. The area occupied by the road is $$1764$$ square metre. What is the perimeter along the outer edge of the road?


Solution

given with of road $$=3m$$
assume Length of outer square is $$4m$$
Then also Length of inner square is $$(n-6) m$$
So area of roads =area of outer square- area of inner square
$$1764=n^2-(n-6)^2$$
$$1764=n^2-(n^2-12n+36)$$
$$1764=12n-36$$
$$12n=1800$$
$$n=150$$
So The perimeter of the park $$=4n$$
                                                 $$=4\times 150$$
                                                 $$=600\ meter$$

1365036_1178398_ans_f7ae70b036284cce9a5dfe338279a125.png

Mathematics

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