Question

in the diagram below, ( \triangle nju sim \triangle kil ). find ( n ).
write your answer as a whole number or a decimal. do not round.
( n=) yards

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle NIJ\sim\triangle KIL\), the ratios of corresponding sides are equal. That is \(\frac{NJ}{KL}=\frac{NI}{KI}\).
We know \(NJ = 50\) yd, \(NI=50\) yd, \(KI = 100\) yd. Let \(KL=n\).

Step2: Substitute values into the proportion

Substituting the values into \(\frac{NJ}{KL}=\frac{NI}{KI}\), we get \(\frac{50}{n}=\frac{50}{100}\).
Cross - multiply: \(50\times100=50\times n\).

Step3: Solve for \(n\)

Divide both sides of the equation \(5000 = 50n\) by \(50\). So \(n=\frac{5000}{50}=100\).

Answer:

\(100\)