Answer:
The equation 0 = 3x² + 17x - 160 could be of use in finding the length.
Step-by-step explanation:
We are told that the area of the vegetable garden is 170 ft².
Now, from the options;
1) For 0 = 3x² + 2x + 180, using quadratic formula, we have:
x = [-2 ± √(3² - 4(3 × 180)]/(2 × 3)
x = [-2 ± √(-2151)]/6
The value inside the square root is negative, thus there is no natural root of x.
Hence, the equation can't be used to find the length.
2) For the equation 0 = 3x² + 10x + 180, using quadratic formula, the value inside the square root would also be negative and as such there is no natural root of x. So this equation can't be used to get the length.
3) For the equation 0 = 3x² + 17x - 160, using quadratic formula, the roots are -10.67 or 5. We can use 5 as it's a whole number. Since the area is also a whole number, then this equation can be used to find the length.
4) For the equation 0 = 3x² - 160, simplifying, we have;
3x² = 160
x² = 160/3
x = ±√(160/3)
x = ±7.303
Since area is a whole number and this length is not, this equation may not be an accurate way to get the length.
