Question

the correct answer in the box. an airplane takes off from point a in a straight line, as shown in the diagram. the distance from a to e is feet. reset next

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABD\) and \(\triangle ACE\) are similar (by AA similarity, as the angles are equal because of the parallel lines and the common angle at \(A\)). The ratio of their corresponding sides is equal. Let \(AE = x\). The ratio of the sides of the smaller triangle to the larger triangle is \(\frac{AB}{AC}=\frac{AD}{AE}\). Given \(AB = 5600\), \(AC=7000\), and \(AD = 5200\).
So, \(\frac{5600}{7000}=\frac{5200}{x}\)

Step2: Solve the proportion for \(x\)

Cross - multiply: \(5600x=7000\times5200\)
First, simplify \(\frac{5600}{7000}=\frac{4}{5}\). The equation becomes \(\frac{4}{5}=\frac{5200}{x}\)
Then \(4x = 5\times5200\)
\(4x=26000\)
\(x=\frac{26000}{4}=6500\)

Answer:

\(6500\)