Questions: Q. Find the missing length.

Solution Steps

Let the missing length be denoted by \(x\). The larger triangle has sides 45 and 27. The smaller triangle has sides 20 and \(x\). We are given that the two triangles are similar since one of the angles is the same (marked with red) and another angle is a right angle in both triangles. So, the ratio of corresponding sides must be the same, giving us the scale factor.

Scale factor \(= \frac{45}{20} = \frac{9}{4}\)

We can set up a proportion to solve for the missing length, $x$. \(\frac{27}{x} = \frac{45}{20}\) Cross-multiply: \(45x = 27 \times 20\) \(45x = 540\) \(x = \frac{540}{45}\) \(x = 12\)

Final Answer