A park square in shape has a 3 , m wide road | vedclass

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(B) Let the side length of the outer square be $x \, m$.Since the road is $3 \, m$ wide and runs along the inside of the square,the side length of the

Vedclass · Accepted Answer

$600$

Vedclass · Answer

(B) Let the side length of the outer square be $x \, m$.Since the road is $3 \, m$ wide and runs along the inside of the square,the side length of the inner square is $(x - 3 - 3) = (x - 6) \, m$.The area of the road is the difference between the area of the outer square and the inner square:$	ext{Area of road} = x^{2} - (x - 6)^{2} = 1764 \, m^{2}$.Using the identity $a^{2} - b^{2} = (a - b)(a + b)$:$(x - (x - 6))(x + (x - 6)) = 1764$$(6)(2x - 6) = 1764$$2x - 6 = \frac{1764}{6} = 294$$2x = 294 + 6 = 300$$x = 150 \, m$.The perimeter along the outer edge of the road is the perimeter of the outer square:$	ext{Perimeter} = 4 	imes x = 4 	imes 150 = 600 \, m$.

$A$ park square in shape has a $3 \, m$ wide road inside it running along its sides. The area occupied by the road is $1764 \, m^{2}$. What is the perimeter along the outer edge of the road? (in $metres$)

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