Question

1. solve for x, to the nearest tenth. use the triangle proportionality theorem.

x =
46
16
20

Explanation:

Step1: Apply the Triangle Proportionality Theorem

The Triangle Proportionality Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. So, we have the proportion \(\frac{x}{x + 20}=\frac{16}{46}\).

Step2: Cross - multiply

Cross - multiplying gives us \(46x=16(x + 20)\).

Step3: Expand the right - hand side

Expanding \(16(x + 20)\) gives \(46x=16x+320\).

Step4: Subtract \(16x\) from both sides

Subtracting \(16x\) from both sides: \(46x-16x = 16x+320 - 16x\), so \(30x=320\).

Step5: Solve for \(x\)

Dividing both sides by \(30\), \(x=\frac{320}{30}\approx10.7\).

Answer:

\(10.7\)