Respuesta :

[tex]y = \frac{x}{2} [/tex]

[tex]2x + 2y = \sqrt{180} \\ = > 2x + 2( \frac{x}{2} ) = \sqrt{180} \\ = > 2x + x = \sqrt{2 \times 2 \times 3 \times 3 \times 5} \\ = > 3x = 2 \times 3\sqrt{5} \\ = > 3x = 6 \sqrt{5} \\ = > x = \frac{6 \sqrt{5} }{3} \\ = > x = 2 \sqrt{5} [/tex]

[tex]x.y \\ = x \times \frac{x}{2} \\ = \frac{ {x}^{2} }{2} \\ = \frac{ {(2 \sqrt{5} )}^{2} }{2} \\ = \frac{4 \times 5}{2} \\ = \frac{20}{2} \\ = 10[/tex]

Answer:

10

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Answer:

b

Step-by-step explanation:

Given

2x + 2y = [tex]\sqrt{180}[/tex] = [tex]\sqrt{36(5)}[/tex] = 6[tex]\sqrt{5}[/tex]

and y = [tex]\frac{x}{2}[/tex] , then

2x + (2 × [tex]\frac{x}{2}[/tex] ) = 6[tex]\sqrt{5}[/tex]

2x + x = 6[tex]\sqrt{5}[/tex]

3x = 6[tex]\sqrt{5}[/tex] ( divide both sides by 3 )

x = 2[tex]\sqrt{5}[/tex]

and y = [tex]\frac{2\sqrt{5} }{2}[/tex] = [tex]\sqrt{5}[/tex]

Then

xy = 2[tex]\sqrt{5}[/tex] × [tex]\sqrt{5}[/tex] = 2 × 5 = 10 → b

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