Respuesta :

Answer:

y = 2√5.

Step-by-step explanation:

Consider the smallest triangle.

Applying Pythagoras theorem:

y^2 = x^2 + 2^2

The smallest and larger triangle (the one with one side = 8) are similar so we have the proportions :

x/2 = 8/x

---> x^2 = 16

---> x = 4.

Therefore , substituting for x  in the first equation:

y^2 = 4^2 + 2^2

---> y^2 = 20

--->  y = √20

---> y =  2√5.

Answer:

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

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(leg of big Δ )² = (part of hypotenuse below it ) × ( whole hypotenuse )

y² = 2 × (2 + 8) = 2 × 10 = 20 ( take square root of both sides )

y = [tex]\sqrt{20}[/tex] = [tex]\sqrt{4(5)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{5}[/tex] = 2[tex]\sqrt{5}[/tex]

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