Question

Quadrilateral DEFG is similar to quadrilateral HIJK. Find the measure of side HI. Figures are not drawn to scale.

Answer 1

The two quaudrilaterals aregiven as similar shapes. That means

$\begin{gathered} DG\cong HK \\ \text{And, DE}\cong HI \\ \text{Therefore the following ratios apply;} \\ \frac{DG}{HK}=\frac{DE}{HI} \\ \frac{63}{21}=\frac{89.1}{HI} \\ \text{Cross multiply and you have,} \\ HI=\frac{89.1\times21}{63} \\ HI=\frac{89.1}{3} \\ HI=29.7 \end{gathered}$

Therefore side HI measures 29.7 units