Tasha is planning an expansion of a square flower garden in a city park. If each side of the original garden is increased by 7 m, the new total area of the garden will be 144 m². Find the length of each side of the original garden.

Question

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Answer 1

Let x be the length of each side of the original garden.

The area of the original garden is x^2.

When each side is increased by 7 m, the new length of each side will be x + 7.

The new area of the garden will be (x + 7)^2 = 144.

Expanding (x + 7)^2, we get x^2 + 14x + 49 = 144.

Subtracting 144 from both sides, we get x^2 + 14x + 49 - 144 = 0.

Simplifying, we get x^2 + 14x - 95 = 0.

Using the quadratic formula to solve for x, we get:

x = (-14 ± √(14^2 - 4*1*(-95))) / 2*1
x = (-14 ± √(196 + 380)) / 2
x = (-14 ± √576) / 2
x = (-14 ± 24) / 2

This gives us two possible values for x:

x = (10/2) or x = (-38/2)

Since the length of each side can't be negative, the original length of each side of the garden is 5 m.