Answer:
Explanation:
You want the missing segment lengths in the kite shown, where half-diagonals are 3 and 6, and one side length is 5.
Kite
The diagonals of a kite cross at right angles, so each of the triangles shown is a right triangle. The figure has left-right symmetry about the vertical axis, so x=z.
Length y
We recognize the top triangles as being 3-4-5 right triangles, so the missing side length is y = 4.
Lengths x and z
These lengths are the hypotenuse of a right triangle with legs 3 and 6. The Pythagorean theorem tells us they are ...
x² = 3² +6²
x² = 9 +36 = 45
x = √(45) = √(9·5) = 3√5
The lengths x and z are ...
x = z = 3√5
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Additional comment
In case you have never heard of a 3-4-5 right triangle, you can find y from the Pythagorean relation:
5² = 3² +y²
y² = 25 -9 = 16
y = √16 = 4
The {3, 4, 5} Pythagorean triple is one of several in common use in algebra, trig, and geometry problems. Others include {5, 12, 13}, {7, 24, 25}, {8, 15, 17}.