Question

find the missing length
u, m, t are on a line segment with um = 28, ut = 49, so mt = 49 - 28 = 21? wait, no, the triangle has sides: uv = 77, the smaller triangle has side 33, and the other side is 42, and we need to find l (the missing length). the options are 20, 13, 18, 9 (wait, maybe i misread, but the main text is find the missing length with the diagram having lengths 77, 33, 28, 49, 42, and a question mark, and options below: 20, 13, 18, 9 (maybe more, but the ocr text here is the problem statement: find the missing length, with the diagrams numbers and the multiple-choice options at the bottom).

Explanation:

Step1: Identify similarity ratio

$\text{Ratio} = \frac{UM}{UT} = \frac{28}{49} = \frac{4}{7}$

Step2: Set up proportion for $L$

$\frac{33}{77} = \frac{L}{42}$

Step3: Solve for unknown length $L$

$L = 42 \times \frac{33}{77} = 42 \times \frac{3}{7} = 18$

Answer:

18