Question

find u.
k
22
j
11
i 14u-6 h u+15 g
u =

Explanation:

Step1: Identify the theorem

By the Basic Proportionality Theorem (Thales' theorem), if a line is drawn parallel to one side of a triangle, intersecting the other two sides, then it divides those sides proportionally. Here, \( JH \parallel KG \), so \(\frac{IJ}{JK}=\frac{IH}{HG}\).

Step2: Substitute the values

We know \( IJ = 11 \), \( JK = 22 \), \( IH = 14u - 6 \), and \( HG = u + 15 \). Substituting these into the proportion: \(\frac{11}{22}=\frac{14u - 6}{u + 15}\). Simplify \(\frac{11}{22}\) to \(\frac{1}{2}\), so we have \(\frac{1}{2}=\frac{14u - 6}{u + 15}\).

Step3: Cross - multiply

Cross - multiplying gives \( 1\times(u + 15)=2\times(14u - 6) \). Which simplifies to \( u + 15 = 28u-12 \).

Step4: Solve for u

Subtract \( u \) from both sides: \( 15=27u - 12 \). Then add 12 to both sides: \( 15 + 12=27u \), so \( 27 = 27u \). Divide both sides by 27: \( u = 1 \).

Answer:

\( u = 1 \)