The width of a rectangle is the length minus 2 units. The area of the rectangle is 35 units. What is the width, in units, of the rectangle?
Mathematics · High School · Tue Nov 03 2020
Answered on
Given:
The width of a rectangle is the length minus 2 units. The area of the rectangle is 35 units.
Determine the width of the rectangle.
Solution:
In order to determine the answer, we must first equate the values in a representation as,
x = length
x - 2 = width
Formula for the area of the rectangle:
A = lw
Equate the values in the given equation.
35 = (x)(x - 2)
35 = x^2 - 2x
= x^2 - 2x - 35
The factors of the quadratic equation can be written as,
= ( x + 5) ( x - 7)
To find for the value of x, we equate the values to 0.
x + 5 = 0
x - 7 = 0
Transpose 5 and -7 to the opposite side of the equation, hence it must be taken to note that in transposing a number, the sign changes.
x = -5
x = 7
Since we cannot have a negative width, then the width is 7.
Final answer:
= 7 units