Question

find y. write your answer as a whole number or a decimal. do not round. y = feet

Explanation:

Step1: Use the similarity of triangles

Since \( \triangle DCE\sim\triangle DBA\) (by AA similarity, as \(\angle D=\angle D\) and \(\angle DEC = \angle DAB=90^{\circ}\)), the ratios of their corresponding sides are equal. That is \(\frac{DE}{DA}=\frac{y}{BA}\).

Step2: Calculate the value of \(DA\)

\(DA=DE + EA=5.5+5.5 = 11\) ft.

Step3: Substitute values into the proportion

We know \(DE = 5.5\) ft, \(DA = 11\) ft, and \(BA=9.6\) ft. Substituting into \(\frac{DE}{DA}=\frac{y}{BA}\), we get \(\frac{5.5}{11}=\frac{y}{9.6}\).

Step4: Solve for \(y\)

Cross - multiply: \(11y=5.5\times9.6\). Then \(y=\frac{5.5\times9.6}{11}\). Since \(5.5=\frac{11}{2}\), then \(y=\frac{\frac{11}{2}\times9.6}{11}\). The \(11\) in the numerator and denominator cancels out, and \(y = 4.8\).

Answer:

\(y = 4.8\) feet