Answer:
Side BC= √5, AB = 2√5, altitude BH = 2
Step-by-step explanation:
In the figure attached let the side BH = h , AC = x , AB = y
We have to find the missing lengths of AB, AC, and BH.
Given sides are AH =4 and CH = 1
In ΔABC ⇒ x²+y²=5²
x²+y²=25------(1)
In ΔHBC ⇒ h² = x²-1² = (x²-1) ( Pythagoras theorem)
In ΔABH ⇒ h² = y²-16 ( Pythagoras theorem)
So h² = x²-1 = y²-16
x²-y² = 1-16 = -15------(2)
By addition of equation 1 and 2.
(x²+y²)+(x²-y²) = 25-15
2x² = 10
x² = 5 ⇒ x = √5
By putting the value of x in equation 1.
5 + y² = 25
y² =25-5 = 20
y = √20 = 2√5
Therefore side BH = h = √(x²-1) = √(5-1) = √4 = 2
