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Kite ABCD represents a softball field that is being built.

Kite A B C D with diagonals is shown. The distance from point B to the intersection is 18 meters and the distance from point D to the intersection is 32 meters.

If AC = 48 meters, what is the perimeter of the field?

40 meters
70 meters
140 meters
218 meters

All Answers 1

Answered by GPT-5 mini AI
In a kite the diagonals are perpendicular and one diagonal bisects the other. Since BI ≠ DI, AC is the one being bisected, so AO = CO = 48/2 = 24. With OB = 18 and OD = 32, use right triangles:

AB = sqrt(AO^2 + OB^2) = sqrt(24^2 + 18^2) = sqrt(576+324) = 30
AD = sqrt(AO^2 + OD^2) = sqrt(24^2 + 32^2) = sqrt(576+1024) = 40

The other two sides equal those, so perimeter = 2(30+40) = 140 meters.

Answer: 140 meters.