Questions: Quadrilateral ABCD is similar to quadrilateral EFGH. Find the measure of side GH. Round your answer to the nearest tenth if necessary.

Solution Steps

Since quadrilateral ABCD is similar to quadrilateral EFGH, the corresponding sides are proportional. The corresponding sides are:

• AB corresponds to EF
• BC corresponds to FG
• CD corresponds to GH
• DA corresponds to HE

We know the lengths of AB and EF, and we need to find the length of GH. The proportion can be set up as follows: \[ \frac{AB}{EF} = \frac{BC}{GH} \] Given:

• \( AB = 5 \)
• \( EF = 21 \)
• \( BC = 2 \)
• \( GH = x \) (unknown)

Using the proportion: \[ \frac{5}{21} = \frac{2}{x} \] Cross-multiply to solve for \( x \): \[ 5x = 2 \times 21 \] \[ 5x = 42 \] \[ x = \frac{42}{5} \] \[ x = 8.4 \]

Final Answer