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3 years ago

In order for the parallelogram to be a rhombus, x=?

Mathematics

1 answer:

Cloud [144]3 years ago

5 0

Answer:

Step-by-step explanation:

The diagonal must be an angle bisector for a rhombus.

That means that both bisected angles are equal.

2x + 16 = 5x - 8 Add 8 to both sides

2x + 16 + 8 = 5x

2x + 24 = 5x Subtract 2x from both sides

24 = 5x - 2x

24 = 3x Divide by 3

24/3 = x

x = 8

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Answer:

The answer to your question is FJ = 18

Step-by-step explanation:

Data

FG = 30

FH = 12

HE = 8

JH ║GE

These triangles are similar, so we can use proportions to find the length of FJ.

$\frac{FJ}{FH} = \frac{FG}{FH + HE}$

Substitution

$\frac{FJ}{12} = \frac{30}{12 + 8}$

Simplification

$\frac{FJ}{12} = \frac{30}{20}$

Solve for FJ

$FJ = 12 \frac{30}{20}$

Result

FJ = 18

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