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
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- The area of the right angled triangle ABC, when base is BC=AB×BC2=128×962=6144 cm2…(1)
- The area of the right angled triangle ABC, when base is AC =AC×BD2=160×BD2…(2)
- Since, the area in the equations (1) and (2) should be the same, equating the area in equation (2), we get:
⟹160×BD2=6144⟹160×BD=12288⟹BD=12288160⟹BD=76.8 cm - Therefore, the length of the perpendicular line from side AC to point B is 76.8 cm.