Questions: Find the length of EH . a. 3 b. 9 c. 21 d. 42

Solution Steps

Given that \( EH = 5x - 3 \) and \( HF = 2x + 24 \), and knowing that \( EH \) and \( HF \) are parts of the same line segment \( EF \), we can set up the equation: \[ EH + HF = EF \]

Substitute \( EH = 5x - 3 \) and \( HF = 2x + 24 \) into the equation: \[ (5x - 3) + (2x + 24) = EF \]

Combine like terms: \[ 5x - 3 + 2x + 24 = EF \] \[ 7x + 21 = EF \]

Since \( EF \) is a line segment, we need to find the value of \( x \) that makes \( EH \) a valid length. We can assume \( EF \) is a specific length, but since it is not given, we solve for \( x \) in terms of \( EF \): \[ 7x + 21 = EF \] \[ 7x = EF - 21 \] \[ x = \frac{EF - 21}{7} \]

Substitute \( x \) back into the expression for \( EH \): \[ EH = 5x - 3 \] \[ EH = 5 \left( \frac{EF - 21}{7} \right) - 3 \] \[ EH = \frac{5(EF - 21)}{7} - 3 \] \[ EH = \frac{5EF - 105}{7} - 3 \] \[ EH = \frac{5EF - 105 - 21}{7} \] \[ EH = \frac{5EF - 126}{7} \]

Final Answer