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 triangle

The sloping side (hypotenuse) is 4 m, height (one leg) is 3 m. Use Pythagorean theorem to find the base of the right triangle: $a = \sqrt{c^2 - b^2}$, where $c = 4$, $b = 3$.
$a = \sqrt{4^2 - 3^2} = \sqrt{16 - 9} = \sqrt{7} \approx 2.6458$ m.

Step2: Calculate the base width of the trapezoid

The top width is 10 m. The base width is top width plus 2 times the base of the right triangle (since there are two sloping sides, each with a right triangle at the base).
Base width $= 10 + 2\times\sqrt{7} \approx 10 + 2\times2.6458 = 10 + 5.2916 = 15.2916$ m.

Answer:

The width at the base of the embankment is approximately $10 + 2\sqrt{7}$ m (or about 15.29 m).