Question

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

Answer 1

Length of BH is 2 units.

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* HC`

i.e.
`BH^(2)=4* 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.