# Perimeter of a kite?

Hey, could anyone here please find the perimeter of this kite? I'm kind of stuck.

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• 2 months ago

A kite has bilateral symmetry, so the two short segments on the perimeter are the same, and the two long segments are the same.

The diagonals cross at right angles forming 2 pairs of right triangles.

Looking at the small triangles on the left, they have legs of 7 and 24. Use the Pythagorean Theorem (or your knowledge of Pythagorean Triples) to find the hypotenuse.

7² + 24² = c²

49 + 576 = c²

c² = 625

c = √625

c = 25

So the two short segments on the perimeter are 25 and 25. The two long segments would be 92.179 and 92.179, as marked.

At this point you can stop and add up the 4 sides and be done.

P = 25 + 25 + 92.179 + 92.179

P = 234.358

However, if they hadn't given you the measurement of the long segments, you could have still figured it out from the two large right triangles on the right.

The full diagonal is 96, so the long leg would be 96-7 = 89. And the short leg is 24.

24² + 89² = d²

576 + 7921 = d²

d² = 8497

d = √8497

d ≈ 92.179

P = 25 + 25 + 92.179 + 92.179

P = 234.358

~234.358

• tomlinson2 months agoReport

thank you so much! that was even more than i needed! i really appreciate it