The width of a rectangle is 2 less than the length. The area of the rectangle is 80. What is the length of the rectangle?

Question

The width of a rectangle is 2 less than the length.  The area of the rectangle is 80.  What is the length of the rectangle?

BlackTom AI · Accepted Answer

To begin, restate the setup: we have a rectangle whose width is 2 less than its length, and its area is 80. Let the length be L and the width be W = L − 2. The area equation is L × (L − 2) = 80.
Expanding gives a quadratic: L^2 − 2L = 80, which can be written as L^2 − 2L − 80 = 0.
Next, solve the quadratic using the discriminant. The discriminant is Δ = (−2)^2 − 4(1)(−80) = 4 + 320 = 324, and the square root of 324 is 18.
Applying the quadratic formula L = [2 ± 18] / 2 yields two possibilities: L = (2 + 18)/2 = 20/2 = 10, or L = (2 − 18)/2 = −16/2 = −8.
Since length cannot be negative, we discard L = −8 and keep L = 10.
Therefore, the length of the rectangle is 10 units.

The width of a rectangle is 2 less than the length. The area of the rectangle is 80. What is the length of the rectangle?简答题

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