Quadrilateral BCDE is similar to quadrilateral FGHI. Find the measure of side HI. Figures are not drawn to scale.
HG: 4.3
ED: 20
DC: 10
Since quadrilateral BCDE is similar to quadrilateral FGHI, the corresponding sides are proportional. Using this information, we can set up the following proportion:
$\frac{BC}{FG}=\frac{DE}{HI}$
We are given that $DE=20$, so we can substitute the value into the equation:
$\frac{BC}{FG}=\frac{20}{HI}$
We are also given that $DC=10$, so we can substitute this value into the equation:
$\frac{10+BC}{FG}=\frac{20}{HI}$
We are given that $HG=4.3$, so we can substitute this value into the equation:
$\frac{10+BC}{4.3}=\frac{20}{HI}$
To solve for HI, we can cross-multiply and solve for HI:
$HI(10+BC)=20(4.3)$
Divide both sides by $10+BC$:
$HI=\frac{20(4.3)}{10+BC}$
We cannot solve for the measure of side HI without knowing the measure of side BC.