Final answer:
The length of each side of the original square garden is 8 meters. We determined this by setting up an equation for the area of the expanded garden as a square of (x + 7), setting it equal to 169 m², and solving for x.
Step-by-step explanation:
Tesha is planning to expand a square garden where each side of the original garden is increased by 7 meters, resulting in a new total area of 169 m². To find the length of each side of the original garden, we begin by understanding that the area of a square is calculated by squaring the length of one of its sides (side × side).
Since each side of the garden is increased by 7 meters, if we let x represent the length of a side of the original square garden, then the length of a side of the new expanded garden would be x + 7 meters.
To find the new total area, we square the new length of a side:
(x + 7 m) × (x + 7 m) = 169 m²
Expanding the equation we get:
x² + 14x + 49 = 169
Subtracting 169 from both sides to solve for x we get:
x² + 14x - 120 = 0
Solving for x using the quadratic formula or by factoring, we find that x = 8 or x = -15. We discard the negative value since the length cannot be negative, leaving us with x = 8 meters as the length of each side of the original square garden.