Question

question
quadrilateral cdef is similar to quadrilateral ghij. find hi. round your answer to the nearest tenth if necessary. figures are not drawn to scale.
(there are two quadrilateral figures, one labeled cdef with side cf=5 and de=8, the other labeled ghij with side gj=19 and hi=x)

Explanation:

Step1: Identify corresponding sides

Since quadrilaterals \( CDEF \) and \( GHIJ \) are similar, their corresponding sides are proportional. Let's assume \( CF \) corresponds to \( GJ \) and \( DE \) corresponds to \( HI \). Given \( CF = 5 \), \( GJ = 19 \), and \( DE = 8 \), we need to find \( HI = x \).

Step2: Set up proportion

The ratio of corresponding sides should be equal. So, \(\frac{CF}{GJ}=\frac{DE}{HI}\) which translates to \(\frac{5}{19}=\frac{8}{x}\).

Step3: Solve for \( x \)

Cross - multiply: \( 5x=19\times8 \)
\( 5x = 152 \)
Divide both sides by 5: \( x=\frac{152}{5}=30.4 \)

Answer:

\( 30.4 \)