Respuesta :

Answer:

A

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to find EF

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

EF² + DF² = DE² ← substitute values

EF² + 12² = 18², that is

EF² + 144 = 324 ( subtract 144 from both sides )

EF² = 180 ( take the square root of both sides )

EF = [tex]\sqrt{180}[/tex] → A

The required length of EF in right triangle is [tex]\sqrt{180}[/tex].

Given that,

In right triangle; length of DF is 18,

And length of FD is 12.

We have to determine,

The length of EF in the right triangle.

According to the question,

The length of EF in the right triangle is determined by using Pythagoras theorem;

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

[tex](Length\ of \ DE )^2= (Length\ of \ EF )^2+ (Length\ of \ DF )^2[/tex]

Where, length of DE is 18, and length of DF is 12.

Therefore,

Substitute the values in the formula;

[tex]( DE )^2= (EF )^2+ (DF )^2\\\\(18)^2 = (EF)^2 + (12)^2\\\\324 = (EF)^2 + 144\\\\324 - 144 = (EF)^2\\\\(EF)^2 = 180\\\\EF = \sqrt{180}[/tex]

Hence, The required length of EF in right triangle is [tex]\sqrt{180}[/tex].

To know more about Pythagoras theorem click the link given below.

https://brainly.com/question/12504943

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