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
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