Question

find g.
write your answer as a whole number or a decimal. do not round.
g = \boxed{} meters
submit

Explanation:

Step1: Identify Similar Triangles

Triangles \( \triangle LMN \) and \( \triangle JMK \) are similar (by AA similarity, as they have right angles and shared angles). So, the ratios of corresponding sides are equal: \( \frac{LN}{JK} = \frac{NM}{MK} \).

Step2: Substitute Known Values

We know \( LN = 34 \, \text{m} \), \( JK = 51 \, \text{m} \), \( MK = 24 \, \text{m} \), and \( NM = g \). Substituting into the ratio: \( \frac{34}{51} = \frac{g}{24} \).

Step3: Solve for \( g \)

Cross - multiply: \( 51g = 34\times24 \). Calculate \( 34\times24 = 816 \). Then, \( g=\frac{816}{51}=16 \).

Answer:

\( 16 \)