Question

1. δmnp ~ δqrp; find pr

Explanation:

Step1: Set up proportion

Since $\triangle MNP\sim\triangle QRP$, the ratios of corresponding - sides are equal. So, $\frac{NP}{RP}=\frac{MP}{QP}$. Substituting the given values, we get $\frac{x + 8}{3x-9}=\frac{24}{28}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{x + 8}{3x-9}=\frac{24}{28}$ gives us $28(x + 8)=24(3x-9)$.
Expand both sides: $28x+224 = 72x-216$.

Step3: Solve for x

First, move the x - terms to one side and the constants to the other side:
$224 + 216=72x-28x$.
$440 = 44x$.
Divide both sides by 44: $x = 10$.

Step4: Find PR

We know that $PR=3x - 9$. Substitute $x = 10$ into the expression for $PR$.
$PR=3\times10-9$.
$PR=30 - 9$.
$PR = 21$.

Answer:

$21$