Answer:
The dimensions are 11 cm by 15 cm
Step-by-step explanation:
Area of a rectangle = (length)(width).
Let L represent the length and W the width.
Since L = W - 4, we have
Area of rectangle = (W - 4)W = 165 cm^2.
Thus, w^2 - 4W - 165 = 0. We can solve for W using the quadratic formula:
a = 1, b = -4 and c = -165. Thus,
-(-4) ± √ [ (-4)² - 4(1)(-165) ]
W = ---------------------------------------
2
4 ± √ [16 + 660 ]
W = ------------------------------
2
4 ± √ [ 676 ] 4 ± 26
W = ----------------------- = W = ------------- = W = 2 ± 13
2 2
Thus, W is 2 + 13 = 15. It cannot be negative, so we discard 2 - 13 = -11.
If the width, W, is 15, then the length is 4 less, or L = 11.
The dimensions are 11 cm by 15 cm
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