Practise the method.Example 1A rectangle is 7cm by 24cm. Find the diagonal x, in cm.Rectangle with diagonalRectangle with diagonalRectangle with diagonal. Horizontal side 7 cm; vertical side 24 cm. Diagram not to scale. Use the labelled measurements.7 cm24 cmx cmDiagram not to scaleShow worked answerAnswer: 25The diagonal is the hypotenuse of a right triangle.x=√72+242=25cm.Example 2A 39m ladder leans against a vertical wall. Its foot is 15m from the wall on level ground. How high up the wall does it reach, in m?Right triangleRight triangleRight triangle, right angle at the lower left. Horizontal leg 15 m; vertical leg x m; hypotenuse 39 m. Diagram not to scale. Use the labelled measurements.15 mx m39 mDiagram not to scaleShow worked answerAnswer: 36The wall and ground form a right angle.Height =√392−152=36m.Example 3A cuboid has perpendicular dimensions 6cm,8cm and 24cm. Find its space diagonal x, joining opposite corners through the solid, in cm.CuboidCuboidCuboid with front width 6 cm, vertical height 24 cm and depth 8 cm. Diagram not to scale. Use the labelled measurements.6 cm24 cm8 cmx cmDiagram not to scaleShow worked answerAnswer: 26Apply Pythagoras twice: x2=62+82+242=676x=26cm.