Answer:
The answer to your question is width = 8 ft
Explanation:
Data
width = x - 7
length = base = x
Area = 120 ft²
Process
1.- Write the formula of the area of a rectangle
Area = base x width
- Substitution
120 = x (x - 7)
2.- Solve for x
120 = x² - 7x
x² - 7x - 120 = 0
- Factor the polynomial
- Find the prime factors of 120
120 2
60 2
30 2
15 3
5 5
1
- Find two numbers that added gives -7
These numbers are -15 and + 8
- Factor
x² - 15x + 8x - 120
x(x - 15) + 8(x - 15)
(x - 15)(x + 8) = 0
x₁ = 15 x₂ = -8
-The length of the base is 15 because there are no negative lengths.
3.- Conclusion
Base = 15
Width = 15 - 7 = 8