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GB-33-07-001 · Three-dimensional Pythagoras

A cuboid measures 16 cm by 7 cm by 19 cm. Find the length of its longest internal diagonal to 1 decimal place.

3D Pythagoras Booklet p. 34
Method
1) Apply Pythagoras on base rectangle (a² + b²), then with vertical height c
2) Use d² = a² + b² + c² and square root
Worked Example (GB-33-07-001)
Booklet p. 34: Label Hypotenuse H\mathbf{H} (opposite right angle) and use H2=A2+B2\mathbf{H^2 = A^2 + B^2}
1) Apply Pythagoras to a base diagonal and then to the vertical triangle.
2) d2=162+72+192d^2=16^2+7^2+19^2
3) 25.8 cm
25.8 cm