Question

In triangle △ABC, ∠ABC=90°, BH is an altitude. Find the missing lengths. AH=4 and HC=1, find BH.

Answer 1

Answer:

Length of BH is 2 units.

Step-by-step explanation:

We have, ΔABC with ∠ABC = 90° and an altitude BH.

Also, it is given that the length of sides AH is 4 units and HC is 1 units.

Since, the 'Altitude Rule' states that 'the length of the altitude is the geometric mean of the line segments it bisects'.

So, we get that,

$BH^{2}=AH\times HC$

i.e. $BH^{2}=4\times 1$

i.e. $BH^{2}=4$

i.e. $BH=\pm 2$

Since, the length of the side cannot be negative.

So, length of BH is 2 units.