Question

sofia cuts a piece of felt in the shape of a kite for an art project. the top two sides measure 20 cm each and the bottom two sides measure 13 cm each. one diagonal, \\(\overline{eg}\\), measures 24 cm.

what is the length of the other diagonal, \\(\overline{df}\\)?

5 cm
16 cm
21 cm
32 cm

Explanation:

Determine the intersection properties of the diagonals

Let \(H\) be the intersection point of the diagonals \(\overline{EG}\) and \(\overline{DF}\). Since \(DEFG\) is a kite with \(FE = FG = 20\text{ cm}\) and \(DE = DG = 13\text{ cm}\), the diagonal \(\overline{DF}\) is the perpendicular bisector of the diagonal \(\overline{EG}\).

$$
LATEXBLOCK0
$$

Calculate the lengths of the segments of diagonal DF

Apply the Pythagorean theorem to the right triangles \(\triangle EHF\) and \(\triangle EHD\):

$$
LATEXBLOCK1
$$

Find the total length of diagonal DF

Sum the two segments to find the total length of \(\overline{DF}\):

$$ DF = FH + DH = 16 + 5 = 21\text{ cm} $$

Answer:

• 5 cm
• 16 cm
• 21 cm (Correct answer)
• 32 cm