Answer:
The correct answer is option b. 10 cm and 12 cm.
Explanation:
Let's denote the width of the rectangle as "w" and the length as "l".
According to the given information, the area of the rectangle is 120 cm², so we have the equation:
l * w = 120
Additionally, it is stated that the length of the rectangle is eight less than twice the width:
l = 2w - 8
Now we can substitute the value of "l" from the second equation into the first equation:
(2w - 8) * w = 120
Expanding the equation:
2w² - 8w = 120
Rearranging the equation to a quadratic form:
2w² - 8w - 120 = 0
Dividing the equation by 2 to simplify it:
w² - 4w - 60 = 0
To solve this quadratic equation, we can either factorize it or use the quadratic formula. Let's factorize it:
(w - 10)(w + 6) = 0
Setting each factor equal to zero, we have two possibilities:
w - 10 = 0 --> w = 10
w + 6 = 0 --> w = -6 (discarded since width can't be negative)
Therefore, the width of the rectangle is 10 cm.
Substituting this value back into the equation l = 2w - 8:
l = 2(10) - 8
l = 20 - 8
l = 12
So, the dimensions of the rectangle are width = 10 cm and length = 12 cm.