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14. The diagonals of square ABCD intersect at E. If AE = 2, find the perimeter of ABCD.

14 The Diagonals Of Square ABCD Intersect At E If AE 2 Find The Perimeter Of ABCD class=

Sagot :

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Answer:

B, [tex]8\sqrt{2}[/tex]

Step-by-step explanation:

Diagonals of a square are congruent so AC= 4

using pythagorean theorem we can then do [tex]x^{2} +x^{2}[/tex]=[tex]4^{2}[/tex]

[tex]2x^{2} = 16\\x^{2} =8\\x=\sqrt{8} \\x=2\sqrt{2}[/tex]

Then for perimeter we times the [tex]2\sqrt{2}[/tex] by 4 and get

[tex]8\sqrt{2}[/tex]

Hope this helps and please mark brainliest!!

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