Question

find p.
write your answer as a whole number or a decimal. do not round.
p = meters

Explanation:

Step1: Use the similarity of triangles

Since \(\angle CDE=\angle ADB = 90^{\circ}\), \(\angle CED=\angle ABD\) (given), and \(\angle DCE=\angle DAB\) (by the property of angles in a right - angled situation), \(\triangle CDE\sim\triangle ADB\).
For similar triangles, the ratios of corresponding sides are equal. That is \(\frac{CE}{AB}=\frac{CD}{AD}\).
We know \(CE = 8.5\space m\), \(CD=7.5\space m\), \(AD = 13.5\space m\), and \(AB=p\).

Step2: Substitute the values into the proportion

Substituting the values into \(\frac{CE}{AB}=\frac{CD}{AD}\), we get \(\frac{8.5}{p}=\frac{7.5}{13.5}\).
Cross - multiply: \(7.5p=8.5\times13.5\).
First, calculate \(8.5\times13.5=(8 + 0.5)\times13.5=8\times13.5+0.5\times13.5=108+6.75 = 114.75\).
Then, solve for \(p\): \(p=\frac{114.75}{7.5}\).
\(p = 15.3\).

Answer:

\(p = 15.3\) meters