Find the length of BC in the following figure.
Answers
Answer:
BC=14
Step-by-step explanation:
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GiveN:-
- AB = 13 cm
- BO = 5 cm
- AC = 15 cm
- AO is perpendicular to the line BC.
To FinD:-
The length of line BC.
SolutioN:-
Analysis :
AO is perpendicular to line BC so ∆AOB and ∆AOC both are right angled triangle. So, by using Pythagoras Theorem, we can first find the length of AO and then again by using the Pythagoras Theorem we find the length of OC. After this whole calculation, we have to add BO and OC for our required answer i.e., the length of BC.
Solution :
For ∆AOB,
Let the side be "s" cm.
We know that if the triangle is right angled triangle and we are given the hypotenuse and base of the triangle and the side is asked to find then,
By Pythagoras Theorem,
(Hypo)² = (Base)² + (Side)²
where,
- Hypo is hypotenuse = 13 cm
- Base = 5 cm
- Side = s cm
By using the required formula for Pythagoras theorem and substituting the respective values,
⇒ (AB)² = (BO)² + (AO)²
⇒ (13)² = (5)² + (s)²
⇒ 169 = 25 + (s)²
⇒ 169 - 25 = (s)²
⇒ 144 = (s)²
Square rooting both the sides,
⇒ √144 = s
⇒ 12 = s
∴ Side (AO) = 12 cm.
For ∆AOC,
Let the base be "b" cm.
We know that if the triangle is right angled triangle and we are given the hypotenuse and side of the triangle and the base is asked to find then,
By Pythagoras Theorem,
(Hypo)² = (Base)² + (Side)²
where,
- Hypo is hypotenuse = 15 cm
- Side = 12 cm
- Base = b cm
By using the required formula for Pythagoras theorem and substituting the respective values,
⇒ (AC)² = (OC)² + (AO)²
⇒ (15)² = (b)² + (12)²
⇒ 225 = (b)² + 144
⇒ 225 - 144 = (b)²
⇒ 81 = (b)²
Square rooting both the sides,
⇒ √81 = b
⇒ 9 = b
∴ Base (OC) = 9 cm.
Length of BC :
- Length of BO = 5 cm
- Length of OC = 9 cm
So,
Length of BC = BO + OC
= 5 + 9
= 14 cm