Question

The perimeter of a square garden is 12 meters greater than the perimeter of a smaller square garden. The area of the larger garden is 105 greater than that of the smaller garden. Find the dimension of the larger garden. (EXPLAIN STEPS)

Answer 1

Answer: 19 by 19 meters

Explanation:

The perimeter of a square is given by 4 * side_length. So, the perimeter of the larger square is 4y and the perimeter of the smaller square is 4x. According to the problem, 4y = 4x + 12. We can simplify this to y = x + 3.

The area of a square is given by side_length^2. So, the area of the larger square is y^2 and the area of the smaller square is x^2. According to the problem, y^2 = x^2 + 105.

Now we can substitute y = x + 3 from the first equation into the second equation:

(x + 3)^2 = x^2 + 105

Expanding and simplifying gives us:

x^2 + 6x + 9 = x^2 + 105

Subtracting x^2 from both sides gives:

6x + 9 = 105

Subtracting 9 from both sides gives:

6x = 96

Finally, dividing both sides by 6 gives:

x = 16

Substituting x = 16 into y = x + 3 gives y = 19.

So, the side length of the larger garden is 19 meters.