Question
Find the value of x for which ABCD must be a parallelogram.
(5x-3)
(14x-48)
22
5
12
3
Answers
GPT-4o
To determine the value of \( x \) for which ABCD is a parallelogram, you need to use the properties of a parallelogram. One key property is that opposite sides of a parallelogram are equal in length.
Assume the given side lengths are for opposite sides of the parallelogram:
1. \( 5x - 3 \)
2. \( 14x - 48 \)
Since these are opposite sides, they must be equal:
\[ 5x - 3 = 14x - 48 \]
Now, solve the equation for \( x \):
1. Subtract \( 5x \) from both sides to get:
\[ -3 = 9x - 48 \]
2. Add 48 to both sides to get:
\[ 45 = 9x \]
3. Divide both sides by 9 to find \( x \):
\[ x = 5 \]
Therefore, the value of \( x \) for which ABCD must be a parallelogram is \( 5 \).
Assume the given side lengths are for opposite sides of the parallelogram:
1. \( 5x - 3 \)
2. \( 14x - 48 \)
Since these are opposite sides, they must be equal:
\[ 5x - 3 = 14x - 48 \]
Now, solve the equation for \( x \):
1. Subtract \( 5x \) from both sides to get:
\[ -3 = 9x - 48 \]
2. Add 48 to both sides to get:
\[ 45 = 9x \]
3. Divide both sides by 9 to find \( x \):
\[ x = 5 \]
Therefore, the value of \( x \) for which ABCD must be a parallelogram is \( 5 \).