A tennis court has a length of $$ x \mathrm{~cm} $$ and the breath of $$ y \mathrm{~m} $$. It has an area of $$ 40 \mathrm{~m}^{2} $$ and a perimeter of 28 cm . Determine the values of $$ x $$ and $$ y $$.

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To determine the values of $$ x $$ and $$ y $$, we can use the given information about the area and perimeter of the tennis court.

Given:
- Area of the tennis court = $$ 40 \, \text{m}^2 $$
- Perimeter of the tennis court = $$ 28 \, \text{cm} $$

We know that the area of a rectangle (such as a tennis court) is given by the formula:
$$ \text{Area} = \text{Length} \times \text{Breath} $$

And the perimeter of a rectangle is given by the formula:
$$ \text{Perimeter} = 2 \times (\text{Length} + \text{Breath}) $$

Let's denote the length of the tennis court as $$ x $$ cm and the breath as $$ y $$ m. We can set up the equations based on the given information and solve for $$ x $$ and $$ y $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}xy=40\x+2\left(x+y\right)=28\end{array}\right.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}xy=40\x=\frac{-2y+28}{3}\end{array}\right.$$
- step2: Substitute the value of $$x:$$
  $$\frac{-2y+28}{3}\times y=40$$
- step3: Simplify:
  $$\frac{y\left(-2y+28\right)}{3}=40$$
- step4: Cross multiply:
  $$y\left(-2y+28\right)=3\times 40$$
- step5: Simplify the equation:
  $$y\left(-2y+28\right)=120$$
- step6: Expand the expression:
  $$-2y^{2}+28y=120$$
- step7: Move the expression to the left side:
  $$-2y^{2}+28y-120=0$$
- step8: Multiply both sides:
  $$2y^{2}-28y+120=0$$
- step9: Solve using the quadratic formula:
  $$y=\frac{28\pm \sqrt{\left(-28\right)^{2}-4\times 2\times 120}}{2\times 2}$$
- step10: Simplify the expression:
  $$y=\frac{28\pm \sqrt{\left(-28\right)^{2}-4\times 2\times 120}}{4}$$
- step11: Simplify the expression:
  $$y=\frac{28\pm \sqrt{-176}}{4}$$
- step12: The expression is undefined:
  $$y \notin \mathbb{R}$$
- step13: The system of equations has no solution in the set of real numbers:
  $$\left(x,y\right) \notin \mathbb{R}^{2}$$
- step14: Alternative Form:
  $$\textrm{No real solution}$$
The system of equations does not have real solutions. This means that the given information does not lead to a unique solution for the values of $$ x $$ and $$ y $$. Therefore, we cannot determine the exact values of $$ x $$ and $$ y $$ based on the provided information.
There are no real values of $$ x $$ and $$ y $$ that satisfy both the area and perimeter given.

A tennis court has a length of and the breath of . It has an area of
and a perimeter of 28 cm . Determine the values of and .

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A tennis court has a length of and the breath of . It has an area of and a perimeter of 28 cm . Determine the values of and .