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sergiy2304 [10]
2 years ago
15

Does dose anyone know how to solve this?

Mathematics
1 answer:
solniwko [45]2 years ago
6 0

Answer:

Width of rectangle = 6 m

Length of rectangle = 11 m

Step-by-step explanation:

Let width of rectangle = w

Length of rectangle = 3w-7

Area of rectangle = 66 m²

We need to find length and width of rectangle

The formula used is: Area=Length \times Width

Putting values and finding w

Area=Length \times Width\\66=(3w-7)(w)\\66=3w^2-7w\\3w^2-7w-66=0\\

Solve using quadratic formula: w=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

We have a=3, b=-7, c=-66

Putting values and finding w

w=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\w=\frac{-(-7)\pm\sqrt{(7)^2-4(3)(-66)}}{2(3)}\\w=\frac{7\pm\sqrt{49+792}}{6}\\w=\frac{7\pm\sqrt{841}}{6}\\w=\frac{7\pm29}{6}\\w=\frac{7+29}{6}\:,\:w=\frac{7-29}{6}\\w=6, w=-3.6

We get values of w as w=6 and w=-3.6

As we know width cannot be negative, so considering w = 6

So, Width = 6

Length = 3w-7 = 3(6)-7 = 18-7 = 11

So, Width of rectangle = 6 m

Length of rectangle = 11 m

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