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The area of a rectangle is 120 cm2. The length of the rectangle is eight less than the twice of the width. Find the dimensions of the rectangle.a. 6 cm and 20 cm

b. 10 cm and 12 cm
c. 40 cm and 30 cm
d. 5 cm and 24 cm

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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.

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