Question

Quadrilateral FGHI is similar to quadrilateral JKLM. Find the measure of side LM. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.

Answer 1

We can see that side FG is corresponding to side KJ, the ratio between them is 5:24. Since the figures are similar we see that sides IH and LM must have the same ratio. So, we can formulate the following equation.

`\begin{gathered} (FG)/(KJ)=(HI)/(LM) \\ (5)/(24)=(8)/(LM)\text{ (Replacing)} \\ (5)/(24)\cdot LM=8\text{ ( Multiplying by LM on both sides of the equation)} \\ 5\cdot LM=8\cdot24\text{ (Multiplying by 24 on both sides of the equation)} \\ LM=(192)/(5)\text{ (Dividing by 5 on both sides of the equation)} \\ LM=\text{ 38.4 (Dividing)} \\ \text{The answer is 38.4 (Rounding to the nearest tenth)} \end{gathered}`