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EF = 20 cm

Step-by-step explanation:

Here, we want to find the length of EF

To do this, we use the principle of similar triangles

The similar triangles we are considering here will be ;

FEA and FBD

when two triangles are similar, the ratio of their corresponding sides are equal

Let us calculate DC first

we can use Pythagoras’ theorem here and it is that the square of the hypotenuse equals the sum of the square of the two other sides

Using the triangle EDC

15^2 = 12^2 + DC^2

DC^2 = 225-144

DC^2 = 81

DC = 9

So the entire length of BD is 9 + 12 = 21 cm

Thus, we have it that;

Let EF be x

so DF = 15 + x

Hence;

BD/DF = AE/EF

21/15+x = 12/x

21x = 12(15 + x)

21x = 180 + 12x

21x-12x = 180

9x = 180

x = 180/9

x = 20 cm

EF = 20 cm

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step-by-step explanation:

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