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Properties of squares

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

User Akin Ozer
by
6.3k points

1 Answer

8 votes

*see attachement for diagram

Answer:

HG = 25.6

Explanation:

Given:

DE = 16x - 3

EF = 9x + 11

DF = 52

Required:

HG

SOLUTION:

✔️First, find the value of x

Thus, since DE is congruent to EF, therefore:

16x - 3 = 9x + 11

Collect like terms

16x - 9x = 3 + 11

7x = 14

Divide both sides by 7

x = 2

✔️Find EH:

Since diagonals of a rhombus are perpendicular, therefore ∆EHF is a right triangle.

Thus, we would use pythagorean theorem to find EH

EH² = EF² - HF²

EF = 9x + 11

Plug in the value of x

EF = 9(2) + 11 = 18 + 11

EF = 29

HF = 52/2 = 26 (diagonals bisect each other)

EH² = 29² - 26² = 165

EH = √165

EH = 12.8 (nearest tenth)

✔️Find HG:

HG = 2(EH) (diagonals bisect each other)

HG = 2(12.8)

HG = 25.6

Properties of squares If DE = 16x - 3, EF = 9x + 11, and DF = 52, find HG.​-example-1
User Darryl Johnson
by
6.0k points
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