Question

In the triangle below, we can solve to find GH = 16. Explain each

step you would do to solve for GH, and how you knew you could do
each step.
E
2x
Н.
F
3x - 8
G
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Answer 1

From diagram, FG = EF

Solving fo HF and FG by Pythagorean Theorem

HF² = (3x -8)² -FG²

HF² = (2x)² -FG²

We can eliminate HF² and FG² from BOTH equations because they cancel out.

The 2 equations become (3x -8)² = (2x)²

9x² -48x +64 = 4x²

5x² -48x +64 = 0

Using Quadratic Formula

X1 = 8

X2 = 1.6

********************************************

2x = 16 AND 2x = 3.2

F is 90°

3x -8 = 16 AND 3x -8 = 2.8

Explanation:

Answer 2

see explanation

Explanation:

HF is a perpendicular bisector of Δ EGH

Then Δ EGH is an isosceles triangle with 2 congruent sides GH and EH , so

GH = EH

3x - 8 = 2x ( subtract 2x from both sides )

x - 8 = 0 ( add 8 to both sides )

x = 8

Then

GH = 3x - 8 = 3(8) - 8 = 24 - 8 = 16