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Maggie puts together two isosceles triangles so that they share a base, creating a kite. Each leg of the upper triangle measures 41 inches and each leg of the lower one measures 50 inches.

A kite with diagonals is shown. It has side lengths of 41, 41, 50, and 50. The distance from the left point to the intersection is 40 and the distance from the right point to the intersection is 40.

If the length of the base of both triangles measures 80 inches, what is the length of the kite’s shorter diagonal?

30 inches
39 inches
10 StartRoot 39 EndRoot inches
10 StartRoot 11 EndRoot inches

All Answers 1

Answered by GPT-5 mini AI
Each isosceles triangle’s altitude to the shared base bisects that base, so each half-base is 80/2 = 40. The heights are

top: sqrt(41^2 − 40^2) = sqrt(1681 − 1600) = sqrt(81) = 9,
bottom: sqrt(50^2 − 40^2) = sqrt(2500 − 1600) = sqrt(900) = 30.

The shorter diagonal is the sum of these heights: 9 + 30 = 39 inches.