Question

find the missing length indicated.1)

Explanation:

Step1: Apply the basic proportionality theorem (Thales' theorem)

If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides those sides proportionally. Let the missing length be \(x\).
We have the proportion \(\frac{22 - 8}{22}=\frac{x}{x + 35}\)

Step2: Cross - multiply

\((22-8)(x + 35)=22x\)
\(14(x + 35)=22x\)
\(14x+490 = 22x\)

Step3: Solve for \(x\)

\(22x-14x=490\)
\(8x = 490\)
\(x=\frac{490}{8}=61.25\)

Answer:

\(61.25\)