Question

1. a railroad embankment has the shape of a trapezoid with a horizontal top 10 m across, sloping sides each 4 m in length, and a height of 3 m. determine the width at the base of the embankment.

Explanation:

Step1: Analyze the trapezoid's side

We can consider the sloping side, height, and the horizontal segment (let's call it \(x\)) as a right triangle. Using the Pythagorean theorem \(a^2 + b^2 = c^2\), where \(c = 5\) m (length of sloping side), \(b = 3\) m (height), we find \(x\).
\(x=\sqrt{5^{2}-3^{2}}=\sqrt{25 - 9}=\sqrt{16}=4\) m.

Step2: Calculate the base width

The top width is \(10\) m. The base width is the top width plus \(2x\) (since there are two sloping sides, each contributing an \(x\) to the base width).
Base width \(= 10+2\times4 = 10 + 8=18\) m.

Answer:

The width at the base of the embankment is \(18\) meters.