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

A. 19 m
B. 12 m
C. 5 m
D. radical 5 m

Answer 1

Let x be the length of each side of the original garden. Then the area of the original garden is x^2.

If each side is increased by 7 m, then the new length of each side is x+7. The new total area is (x+7)^2 = x^2 + 14x + 49.

We know that the new total area is 144 m², so we can set up an equation:

x^2 + 14x + 49 = 144

Simplifying this equation:

x^2 + 14x - 95 = 0

We can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Plugging in a=1, b=14, and c=-95, we get:

x = (-14 ± sqrt(14^2 - 4(1)(-95))) / 2(1)

x = (-14 ± sqrt(676)) / 2

x = (-14 ± 26) / 2

x = 6 or x = -20

Since we're looking for a length, we can ignore the negative solution and conclude that the length of each side of the original garden is 6 meters.

Answer: none of the given options (missing option E: 6 m).

Answer 2

AAAaannndd the bot gets it wrong yet again!

(x+7)^2 = 144
x+7 = 12
x = 5

Answer 3

I apologize for the error in my previous response. Yes, you are correct that the solution can be obtained by setting up the equation (x+7)^2 = 144 and solving for x, which gives x = 5. Therefore, the length of each side of the original garden is 5 meters.

The correct answer is C. 5 m. Thank you for bringing this to my attention.