Answer:
6 units
Step-by-step explanation:
Remember the formula for the area of a rectangle: A = lw
What we know:
A=48
w = l-2
Substitute A for 48 and w for l-2 into the equation
A = lw
48 = l(l-2) Use the distributive property. Multiply over the brackets.
48 = l² - 2l
Rearrange the equation to standard form (0 = ax² + bx + c) to use quadratic formula.
0 = l² - 2l - 48
a = 1 ; b = -2 ; c = -48 State the variables for the quadratic formula
Substitute a, b and c to find the length:
[tex]l = \frac{-b± \sqrt{b^{2}-4ac} }{2a}[/tex]
[tex]l = \frac{-(-2)± \sqrt{(-2)^{2}-4(1)(-48)} }{2(1)}[/tex] Simplify
[tex]l = \frac{2± \sqrt{4-(-192)} }{2}[/tex]
[tex]l = \frac{2± \sqrt{196} }{2}[/tex]
[tex]l = \frac{2± 14 }{2}[/tex]
Split the equation at the ± for adding and subtracting. Then decide which answer is correct, or if both of them are possible answers.
[tex]l = \frac{2- 14 }{2}[/tex]
[tex]l = \frac{-12 }{2}[/tex]
[tex]l = -8[/tex] This is "inadmissable", or impossible because the length can't be a negative value.
[tex]l = \frac{2+ 14 }{2}[/tex]
[tex]l = \frac{16 }{2}[/tex]
[tex]l = 8[/tex] Length of the rectangle
Use the formula for the area of a rectangle
Substitute the length and area, then isolate "w" for the width
A = lw
48 = (8)w
48/8 = w
w = 6
Therefore the length of the rectangle is 6 units.
