Charlene puts together two isosceles triangles so that they share a base, creating a kite. The legs of the triangles are 10 inches and 17 inches, respectively. If the length of the base for both triangles is 16 inches long, what is the length of the kite’s other diagonal?

The shared base is 16 inches, so its half is 8 inches. In each isosceles triangle, the altitude bisects the base, giving heights of √(10² − 8²) = 6 inches and √(17² − 8²) = 15 inches. The kite’s other diagonal is the distance between the two opposite vertices, so the heights add: 6 + 15 = 21 inches. The answer is 21 inches.

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