Question

In ΔABC, AB = 4 cm, altitude CF = 6 cm and AC = 3 cm. Find the length of altitude BE.

Answer 1

Given: In triangle ABC,

• AB = 4 cm
• Altitude CF = 6 cm   ...(CF ⟂ AB)
• AC = 3 cm
• Find the length of altitude BE   ...(BE ⟂ AC)

Stepwise calculation:

1. Find the length of BC using the fact that the area of ΔABC can be found from the altitude CF on AB:

Area = `1/2 xx AB xx CF`

= `1/2 xx 4 xx 6`

= 12 cm²

2. Use the area to find BC using the altitude BE on AC:

Area = `1/2 xx AC xx BE`

`12 = 1/2 xx 3 xx BE`

⇒ 12 = 1.5 × BE

⇒ `BE = 12 / 1.5`

⇒ BE = 8 cm

3. Optional check for consistency could involve Pythagorean theorem or other relations, but not required here.

The length of the altitude BE is 8 cm.