contestada

Find the value of the variable. Leave your answer in simplest radical form.

a) 2√10

b) 2√5

c) √5

d) √10

i'll give brainliest !! please

Find the value of the variable Leave your answer in simplest radical form a 210b 25c 5d 10ill give brainliest please class=

Respuesta :

clarch19

Answer:

[tex]\sqrt{10}[/tex]

Step-by-step explanation:

This is a 45-45-90 triangle whose leg to hypotenuse ratio is 1 / [tex]\sqrt{2}[/tex]

so I set up a proportion of 1 / [tex]\sqrt{2}[/tex] = x / 2 [tex]\sqrt{5}[/tex]

cross-multiply to get [tex]\sqrt{2}[/tex]x = 2[tex]\sqrt{5}[/tex]

x = 2[tex]\sqrt{5}[/tex] / [tex]\sqrt{2}[/tex] and multiply numerator and denominator by [tex]\sqrt{2}[/tex], this is called rationalizing the denominator

lets do

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

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

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

[tex]\\ \sf\longmapsto x=\sqrt{2(5)}[/tex]

[tex]\\ \sf\longmapsto x=\sqrt{10}[/tex]

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