Question

1. if qp = 15, mn = 20, and ls = 16, calculate the length of sr.

Explanation:

Step1: Assume similar - triangles

Since the lines are parallel, we can assume that $\triangle LQP\sim\triangle LMN$. And the ratio of their corresponding sides is equal. Also, the perpendiculars are related in the same ratio.

Step2: Set up the proportion

The ratio of the sides of the similar triangles gives us $\frac{QP}{MN}=\frac{LS}{LR}$. We know $QP = 15$, $MN=20$, and $LS = 16$. Substituting these values into the proportion $\frac{15}{20}=\frac{16}{LR}$.

Step3: Solve for $LR$

Cross - multiply: $15LR=20\times16$. So, $15LR = 320$, and $LR=\frac{320}{15}=\frac{64}{3}$.

Step4: Calculate $SR$

Since $LR=LS + SR$, then $SR=LR - LS$. Substitute $LR=\frac{64}{3}$ and $LS = 16$ into the equation. $SR=\frac{64}{3}-16=\frac{64 - 48}{3}=\frac{16}{3}$.

Answer:

$\frac{16}{3}$