Complete Question:
The rectangle below has an area of x^2-6x-7 square meters and a width of x-7 meters. What expression represents the length of the rectangle?
Answer:
Solution:
Given that,
[tex]\text{Area of rectangle} = x^2 - 6x - 7 \\\\Width = x - 7[/tex]
TO FIND: LENGTH = ?
We know that,
[tex]Area\ of\ rectangle = length \times width \\\\Therefore\\\\x^2 - 6x - 7 = length \times x - 7\\\\length = \frac{x^2 - 6x - 7 }{x - 7 }\\\\length = \frac{(x-7)(x + 1)}{x - 7}\\\\\text{cancel out x-7 from numerator and denominator} \\\\length = x + 1[/tex]
Thus expression represents the length of the rectangle is (x + 1) meter
