In triangle abc, ab =13 bc = 14 ca = 15 m is the mid point of side ab and h is the foot of the altitude from a to bc, the length of hm is
Answers
Given: A triangle ABC, AB =13 BC = 14 AC = 15 m
To find: length of HM
Solution:
- Now we have given that ABC is a triangle with the sides AB =13 BC = 14 AC = 15.
- Also M is the mid point of side AB and H is the foot of the altitude from A to BC.
- So now, ABH is a right angle triangle.
- Now in right angle triangle, we know that the length of median is half of hypotenuous , so:
MH = AB / 2
= 13 / 2
= 6.5 units
Answer:
So, the length of HM is 6.5 units.
Given : In triangle abc, ab =13 bc = 14 ca = 15 m is the mid point of side ab and h is the foot of the altitude from a to bc
To find : Length of hm
Solution:
ah ⊥ bc
ah² = ac² - ch² = ab² - bh²
Let say bh = x then ch = 14 -x
=> 15² - (14 - x)² = 13² - x²
=> 225 - 196 - x² + 28x = 169 -x²
=> 28x = 140
=> x = 5
hence ah = 12 (ah² = 13² - x²)
area of ΔAhB = (1/2) * 12 * 5 = 30
Lets draw hp⊥ ab
=> Area = (1/2)ab * hp = 30
=> hp = 60/13
bp² = bh² - hp²
=> bp² = 5² - (60/13)²
=> bp = 25/13
m is mid point of ab hence bm = 13/2
mp = bm - bp
=> mp = 13/2 - 25/13
=> mp = (169 - 50)/26
=> mp = 119/26
hm² = mp² + hp²
=> hm² = (119/26)² + (60/13)²
=> hm = 169/26
=> hm = 13/2
=> hm = 6.5
Length of hm = 6.5
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