Question

find u.
write your answer as a whole number or a decimal. do not round.
u = yards

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle XHJ\sim\triangle XLK\) (by AA similarity, as \(\angle X\) is common and \(\angle XHJ=\angle XLK = 90^{\circ}\)), the ratios of corresponding sides are equal. That is \(\frac{XJ}{XK}=\frac{u}{KL}\).
We know that \(XJ = 0.5\) yd, \(XK=0.5 + 1=1.5\) yd, and \(KL = 1.2\) yd.

Step2: Substitute the values into the proportion

Substituting the values into \(\frac{XJ}{XK}=\frac{u}{KL}\), we get \(\frac{0.5}{1.5}=\frac{u}{1.2}\).
Cross - multiply: \(1.5u=0.5\times1.2\).

Step3: Solve for \(u\)

First, calculate \(0.5\times1.2 = 0.6\). Then the equation becomes \(1.5u=0.6\).
Divide both sides by \(1.5\): \(u=\frac{0.6}{1.5}\).
Simplify \(\frac{0.6}{1.5}=\frac{6}{15}=\frac{2}{5}=0.4\).

Answer:

\(u = 0.4\) yards