Question

if mq = 4, np = 18, and lq = 12, calculate the length of lp. assume △lmq ~ △lnp. image not set to scale.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle LMQ\sim\triangle LNP\), the ratios of corresponding sides are equal. That is \(\frac{MQ}{NP}=\frac{LQ}{LP}\).

Step2: Substitute the given values into the proportion

We know \(MQ = 4\), \(NP=18\), and \(LQ = 12\). Substituting these into \(\frac{MQ}{NP}=\frac{LQ}{LP}\), we get \(\frac{4}{18}=\frac{12}{LP}\).

Step3: Solve for \(LP\)

Cross - multiply: \(4\times LP=18\times12\). Then \(4LP = 216\). Divide both sides by 4: \(LP=\frac{216}{4}=54\).

Answer:

\(54\)