Question #37f95

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Answer 1 · 2017-07-31T04:27:34

$length = 5 cm$ $"length = 5 cm"$

$width = 13 cm$ $"width = 13 cm"$

First, right down what you know in terms of variables.

$y = 2 x + 3$ $y = 2x + 3$

$65 = y \cdot x$ $65 = y*x$

Next, choose one variable and substitute it in.

${65 cm}^{2} = (2 x + 3) \cdot x$ $"65 cm"^2 = (2x+3)*x$

${65 cm}^{2} = 2 x^{2} + 3 x$ $"65 cm"^2= 2x^2 +3x$

Move the $65$ $65$ over and we can see the quadratic equation

$2 x^{2} + 3 x - 65 = 0$ $2x^2 +3x - 65 = 0$

Next factor.

$(2 x + 13) (x - 5) = 0$ $(2x+13)(x-5) = 0$

$x = - 13 cm or x = 5 cm$ $x = -"13 cm" or x = "5 cm"$

We know that the $x$ $x$ value cannot be negative in this specific problem so we can eliminate the negative solution.

We plug our value for $x$ $x$ into the first equation.

$y = 2 (5 cm) + 3$ $y = 2("5 cm") + 3$

$y = 13 cm$ $y = "13 cm"$

Now we check

${65 cm}^{2} = 13 cm \cdot 5 cm$ $"65 cm"^2 = "13 cm" * "5 cm"$

which is true.

Thus the length is $5 cm$ $"5 cm"$ and the width is $13 cm$ $"13 cm"$ .