Question

if mq = 16, np = 40, and lq = 20, 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 their corresponding sides are equal. That is \(\frac{MQ}{NP}=\frac{LQ}{LP}\).

Step2: Substitute the given values

We know that \(MQ = 16\), \(NP=40\), and \(LQ = 20\). Substituting these into the proportion \(\frac{16}{40}=\frac{20}{LP}\).

Step3: Cross - multiply

Cross - multiplying gives us \(16\times LP=40\times20\). So \(16LP = 800\).

Step4: Solve for \(LP\)

Divide both sides by \(16\): \(LP=\frac{800}{16}\).

Answer:

\(LP = 50\)