In a right angle triangle with sides 12 cm and 16 cm and hypotenuse 20 cm, the length of altitude drawn on the hypotenuse from the opposite vertex is K. Find the value of K.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 9.6 cm.
In a right-angled triangle, the altitude drawn to the hypotenuse creates three similar triangles.
The area of the original triangle can be calculated using different base-height combinations.
Area of the triangle = (1/2) × base × height
⇒ Area = (1/2) × 12 cm × 16 cm = 96 sq.cm
Area of the triangle = (1/2) × hypotenuse × altitude
⇒ 96 sq.cm = (1/2) × 20 cm × K
⇒ K = (96 sq.cm × 2) / 20 cm
⇒ K = 9.6 cm
Therefore, the length of the altitude (K) is 9.6 cm.