The perimeter of a square garden is 16 m greater than the perimeterof a smaller

Question

The perimeter of a square garden is 16 m greater than the perimeterof a smaller square garden. The area of the larger garden is200m2 greater than that of the smaller garden. Find thedimensions of the larger garden.
If this helps, I have an equation: (x +4)2 -x2 = 200 And somehow to my teacher it equals (x + 4 + x)(x + 4 - x) =200 If someone can either explain this method to me or find adifferent way to solve, it would be much appreciated. Thankyou.
If this helps, I have an equation: (x +4)2 -x2 = 200 And somehow to my teacher it equals (x + 4 + x)(x + 4 - x) =200 If someone can either explain this method to me or find adifferent way to solve, it would be much appreciated. Thankyou.

Explanation / Answer

(x +4)2 - x2 = 200 we will use the identity a2 - b2 = (a+b)(a-b) here a = x + 4 & b = x therefore it becomes (x+4+x)(x+4-x)=200

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