Answer:
Width = 30 cm; length = 63 cm
Step-by-step explanation:
Represent the width by w and the length by 2w+3 (all measured in cm).
The area of this rectangle is A = (length)(width) = (2w+3)(w) = 1890 (all in cm^2).
Simplifying this expression, we get 2w^2 + 3w = 1890; putting this into the standard form of a quadratic, we get 2w^2 + 3w - 1890 = 0
The coefficients of this quadratic are a = 2, b = 3 and c = -1890.
The roots are then:
-3 ± √ (9 - 4(2)(-1890) )
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4, or
-3 ± √15129 -3 ± 123
w = ------------------- = ---------------
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We find and keep only the + w value, since w is a width.
120
w = ---------------- = 30 units.
If the width is 30 units, then the length is 2w+3 cm, or 63 cm.
Note that (30)(63) cm^2 = 1890 cm^2, as specified.
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