Question

the diagram shows the intersections of several straight roads. the avenues run parallel to each other. amana walks along oak from point a to b. to the nearest foot, how far does she walk? 75 ft 226 ft 307 ft 347 ft

Explanation:

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

Since the avenues are parallel, we can set up a proportion. Let the distance from \(A\) to \(B\) be \(x\). The proportion is \(\frac{280}{280 + 140}=\frac{x}{x + 113}\). Cross - multiply: \(280(x + 113)=420x\).

Step2: Expand and solve the equation

Expand \(280(x + 113)\): \(280x+280\times113 = 420x\). Then \(280\times113=420x - 280x\). So \(280\times113 = 140x\).

Step3: Calculate \(x\)

\(x=\frac{280\times113}{140}\). \(280\div140 = 2\), so \(x = 2\times113=226\).

Answer:

226 ft