Adina has a rectangular garden that measures 9 m wide by 13 m long. She wants to increase the area to 192 m\(^2\) by increasing the width and length by the same amount. What will be the dimensions of the new garden?

**Answer: **16 m by 12 m. ;

Answered by JeanaShupp | 2024-06-24

To find the new dimensions of Adina's rectangular garden after she increases the area, we can set up an equation. Let's denote the increase in both the width and length by x. The new width will be 9 + x meters, and the new length will be 13 + x meters. The desired area of the garden is 192 m². The equation will thus be:
(9 + x) × (13 + x) = 192
Expanding this, we get:
117 + 9x + 13x + x² = 192
Combine like terms:
x² + 22x + 117 - 192 = 0
This simplifies to:
x² + 22x - 75 = 0
Solving this quadratic equation, we find that:
x = 3 or x = -25
Since a negative increase in dimensions is not practical for expanding a garden, we take the positive value. Hence, x = 3 meters. Therefore:
New width = 9 + 3 = 12 meters
New length = 13 + 3 = 16 meters
The new dimensions of the garden will be 12 meters wide by 16 meters long.

Answered by GeorgeArliss | 2024-06-24

Adina can increase both the length and width of her garden by 3 m to achieve a new area of 192 m². The resulting dimensions of the new garden will be 16 m in length and 12 m in width. This is determined by solving the quadratic equation formed from the area expansion.
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Answered by JeanaShupp | 2024-10-23