Final answer:
To find the new length of the garden, we set up an equation including the original length and width along with an unknown variable representing the additional length and width. We then solve this equation for the new total area, and add the result to the original length to find the new length.
Step-by-step explanation:
To solve this problem, we first need to understand that the area of a rectangle is calculated by multiplying the length and the width. Holly's original garden has an area of 12m (width) * 14m (length) = 168m².
She wants to increase this area to 255m² by increasing both the width and the length by the same amount. Let's denote this amount as 'x'. So the new width will be (12m + x) and the new length will be (14m + x).
Setting up the equation for the new area, we get: (12m + x) * (14m + x) = 255m². Solving this quadratic equation, we can find the value of x.
However, the question asks for the length of the new garden. So once we have the value of 'x', we add it to the original length of the garden, resulting in the new length being 14m + x.
Learn more about Area and Length Calculation