Question

1. find the value of x, given that

there are some numbers and letters on the triangle - 9, 18, 20, x, n, q, m, p, o
and there are multiple - choice options: 25.5, 10, 13, 20

Explanation:

Step1: Use similar - triangle property

Since $NQ\parallel FP$, $\triangle MNQ\sim\triangle MFP$. The ratios of corresponding sides of similar triangles are equal. That is, $\frac{MN}{MF}=\frac{NQ}{FP}=\frac{MQ}{MP}$.
We know that $MN = 10$, $MF=10 + 8=18$, and $MQ = 20$. Let $MP=x + 20$.
So, $\frac{MN}{MF}=\frac{MQ}{MP}$, substituting the values we get $\frac{10}{18}=\frac{20}{x + 20}$.

Step2: Cross - multiply

Cross - multiplying the equation $\frac{10}{18}=\frac{20}{x + 20}$ gives us $10(x + 20)=18\times20$.
Expanding the left - hand side: $10x+200 = 360$.

Step3: Solve for $x$

Subtract 200 from both sides of the equation: $10x=360 - 200$.
$10x = 160$.
Divide both sides by 10: $x=\frac{160}{10}=16$.

Answer:

16