△ABC is a triangle such that ∠C=90∘. Suppose AC=12 cm,AB=13 cm and the perpendicular distance from C to AB is x cm. Find the value of x.
Answer:
4.62
- We need to find x, the perpendicular distance from C to AB, if ∠C=90∘,AC=12 cm, and AB=13 cm. Let D be the point where the perpendicular from C meets AB.
Let D be the point where the perpendicular from C meets AB.
- Using Pythagoras' theorem in triangle ABC
BC=√132−122=5 - Since,
∠ACB=∠ADC=90∘∠BAC=∠CAD[ Common angle ]∠CBA=∠DCA[ Angle sum property ]△ACB and △ADC are similar by AAA criterion ⟹BCAB=CDAC⟹513=x12⟹x=4.62 - Hence, the value of x is 4.62.