A triangle ABC with ABC=90, has the length of the side AB=128 cm and of BC=96 cm. What is the length of the perpendicular line from side AC to point B?


Answer:

76.8 cm

Step by Step Explanation:

  1. In the right angled triangle ABC,AB=128 cm,BC=96 cm
    Now, AC=(AB)2+(BC)2 (As per Pythagoras Theorem) =(128)2+(96)2=(16384+9216)=(25600)=160 cm
  2.  The area of the right angled triangle ABC, when base is BC=AB×BC2=128×962=6144 cm2(1)
  3.  The area of the right angled triangle ABC, when base is AC =AC×BD2=160×BD2(2)
  4. Since, the area in the equations (1) and (2) should be the same, equating the area in equation (2), we get:
    160×BD2=6144160×BD=12288BD=12288160BD=76.8 cm
  5. Therefore, the length of the perpendicular line from side AC to point B is 76.8 cm.

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