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Assume the figure below is a rhombus:

If DE=16x-3, EF=9x+11, and DF=52, find HG





Assume the figure below is a rhombus: If DE=16x-3, EF=9x+11, and DF=52, find HG ​-example-1

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Answer:

HG = √165 ≈ 12.8

Explanation:

All sides of the rhombus are the same length, so ...

DE = EF

16x -3 = 9x +11

7x = 14

x = 2

DE = 16(2) -3 = 29

Because the diagonals bisect each other, we have ...

HF = DF/2 = 52/2 = 26

We know side GF is 29, so ...

HG² + HF² = GF²

HG² = GF² -HF² = 29² -26² = 165

HG = √165 ≈ 12.8 . . . . rounded to tenths

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