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Diagonals and real situations
Diagonals and real situations
Example 1
A rectangle is 7cm by 24cm. Find the diagonal x, in cm.
Rectangle with diagonalDiagram not to scaleShow worked answer
Answer: 25
- The diagonal is the hypotenuse of a right triangle.
- x=√72+242=25cm.
Example 2
A 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 triangleDiagram not to scaleShow worked answer
Answer: 36
- The wall and ground form a right angle.
- Height =√392−152=36m.
Example 3
A cuboid has perpendicular dimensions 6cm,8cm and 24cm. Find its space diagonal x, joining opposite corners through the solid, in cm.
CuboidDiagram not to scaleShow worked answer
Answer: 26
- Apply Pythagoras twice: x2=62+82+242=676
- x=26cm.
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