Question

The width of a rectangle is the length minus 6 units . The area of the rectangle is 7 square units. What is the length, in units, of the rectangle?

Answer 1

Let the length of the rectangle be L units.

Given, the width of the rectangle is L - 6 units.

Since the area of a rectangle is given by length multiplied by width, we have:
L * (L - 6) = 7
Expanding the equation, we get:
L^2 - 6L = 7
Rearranging the equation, we get a quadratic equation:
L^2 - 6L - 7 = 0
Factoring the quadratic equation, we get:
(L - 7)(L + 1) = 0

From this, we get two possible solutions:
L = 7 or L = -1

Since the length of a rectangle cannot be negative, the length of the rectangle is 7 units.