Respuesta :

Answer:

The length of other side = 4 cm

Step-by-step explanation:

Given :

longest side = H = 8 cm

one side = P = 4√3

The other side will be H² = P² + B²

=> 8² = (4√3)² + B ²

=> 64 = 48 + B²

=> 64 - 48 = B²

=> 16 = B²

=> √16 = B

=> B = 4

Let the lengths of sides be a, b and c (hypotenuse).

Hypotenuse is the longest side , So c = 8.

[tex]\sf{Let \: b = 4\sqrt{3}}[/tex]

From the pythagoras theorem :

[tex]a^2 + b^2= c^2[/tex]

[tex]a^2 + (4\sqrt{3})^2= 8^2[/tex]

[tex]a^2 + 16 (3) = 64[/tex]

[tex]a^2 +48=64[/tex]

[tex]a^2 = 16[/tex]

[tex]a = 16 / 2[/tex]

[tex]a = 4[/tex]

The third side is 4 cm.

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