Question

PQR is an equilateral triangle of side a. Find the length of each altitude.

Answer 1

Answer:

3a²/4

Step-by-step explanation:

Given,

PQ= PR= QR = a

We draw altitude PS perpendicular to QR

In triangle PQS,

PQ²= QS² + PS²___________(i)

SINCE IN AN EQUILATERAL TRIANGLE ALTITUDE AND MEDIAN ARE SAME QS = RS

Therefore QR = 1/2 QS

QS = a/2_______(ii)

From (i) and (ii)

PS² = a² - (a/2)²

PS = √ a² - a²/4

PS= √(4a²-a²)/4

PS = a√3/4

Therefore each of its altitudes are a√3/4