Question

find x.
figure is not drawn to scale
x = m
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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. So, we have the proportion \(\frac{35 + 21}{21}=\frac{x}{15}\).

Step2: Simplify the left - hand side of the proportion

First, calculate \(35+21 = 56\). The proportion becomes \(\frac{56}{21}=\frac{x}{15}\). Simplify \(\frac{56}{21}=\frac{8}{3}\) (by dividing numerator and denominator by 7). So, \(\frac{8}{3}=\frac{x}{15}\).

Step3: Solve for \(x\)

Cross - multiply: \(3x=8\times15\). Then \(3x = 120\). Divide both sides by 3: \(x=\frac{120}{3}\).

Answer:

\(x = 40\)