Numerical answer
In a right-angled triangle, the two sides containing the right angle measure 9 cm and 12 cm. What is the length (in cm) of the perpendicular drawn from the right-angle vertex to the hypotenuse?
Show answer and solution
Answer: 7.2
Hypotenuse = √(9² + 12²) = √225 = 15 cm.
Area computed two ways:
(1/2) × 9 × 12 = (1/2) × 15 × h → 108 = 15h → h = 7.2 cm.
Formula: Altitude to the hypotenuse = (product of legs)/(hypotenuse).
Area computed two ways:
(1/2) × 9 × 12 = (1/2) × 15 × h → 108 = 15h → h = 7.2 cm.
Formula: Altitude to the hypotenuse = (product of legs)/(hypotenuse).
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