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Verified Answer :

MrQuizzical

To solve this you need to know Pythagorean theorem.

First, EG is 24, so the halfway points are 12. Knowing Pythagorean triples, you can use 5,12,13 and 12,16,20.

DF = 5+16
DF = 21

If you don't know Pythagorean triples, I have worked it out on the image attached.

View image MrQuizzical
akposevictor

Applying the Pythagorean theorem, the length of diagonal DF is: C. 21 cm.

What is the Pythagorean Theorem?

The sum of the squares of the two shorter legs of a right triangle equals the square of the length of the longest leg.

Let the point of intersection of the diagonals be O.

Diagonal FD bisects diagonal EG into equal segments EO and OG. EO = OG = 24/2 = 12 cm

Find the lengths of FO and OD using the Pythagorean theorem:

FO = √(20² - 12²) = 16 cm

OD = √(13² - 12²) = 5 cm

Length of diagonal DF = FO + OD = 16 + 5 = 21 cm.

Learn more about the Pythagorean theorem on:

https://brainly.com/question/343682

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