Question

Quadrilateral EFGH is similar to quadrilateral IJKL. Find the measure of side LI. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.

Answer 1

We can see that sides HG and LK have a ratio of 8:31 between them. Since sides HE and LI are corresponding, then they must have the same ratio. So, we can formulate the following equation:

`\begin{gathered} (HG)/(LK)=(HE)/(LI) \\ (8)/(31)=(11)/(LI)\text{ (Replacing)} \\ (8)/(31)\cdot LI=11\text{ (Multiplying by LI on both sides of the equation)} \\ 8\cdot LI=11\cdot31\text{ (Multiplying by 31 on both sides of the equation)} \\ LI=(341)/(8)\text{ (Dividing by 8 on both sides of the equation)} \\ LI=42.625\text{ (Dividing)} \\ \text{The answer is 42.6 (Rounding to the nearest tenth)} \end{gathered}`