Question

ABC is similar to ADEF. Find x. GEOMETRY

Answer 1

The value of x in the given diagram is 10

Similar triangles

From the question, we are to determine the value of the side labeled x

First, we will find the value of side |BC|

By the Pythagorean theorem, we can write that

|BC|² = 12² + 16²

|BC|² = 144 + 256

|BC|² = 400

|BC| = √400

|BC| = 20

Now,

Since ΔABC and ΔDEF are similar, we can write that

|BC| / |EF| = P ΔABC / P ΔDEF

But,

P ΔABC = 12 + 16 + 20 = 48

Thus,

|BC| / |EF| = P ΔABC / P ΔDEF becomes

20/ |EF| = 48/24

20/x = 2

x = 20/2

x = 10

Hence, the value of x in the given diagram is 10

Learn more on Similar triangles here: brainly.com/question/24085502

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