Question

The rectangle below has an area of x^2-6x-7 square meters and a width of x-7 meters

Answer 1

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:

The expression represents the length of the rectangle is (x + 1) meter

Solution:

Given that,

$\text{Area of rectangle} = x^2 - 6x - 7 \\\\Width = x - 7$

TO FIND: LENGTH = ?

We know that,

$Area\ of\ rectangle = length \times width \\\\Therefore\\\\x^2 - 6x - 7 = length \times x - 7\\\\length = \frac{x^2 - 6x - 7 }{x - 7 }\\\\length = \frac{(x-7)(x + 1)}{x - 7}\\\\\text{cancel out x-7 from numerator and denominator} \\\\length = x + 1$

Thus expression represents the length of the rectangle is (x + 1) meter