Find the altitude of an equilateral triangle of side 8 cm
Solution:
Given, the side of an equilateral triangle is 8 cm.
We have to find the altitude of the triangle.
An Equilateral triangle is a triangle in which all three sides are equal and angles are also equal. It is also known as an equiangular triangle because the value of each angle of an equilateral triangle is 60 degrees.
Let us consider an equilateral triangle ABC with sides 8 cm each.
Let AD be the altitude of the triangle.
AD is perpendicular to BC and D is the midpoint of BC.
So, BD = 8/2 = 4 cm.
Since AD⟂BC, △ADB and △ADC are right triangles with right angles at D.
In △ADB,
By using Pythagoras theorem,
AB² = BD² + AD²
(8)² = (4)² + AD²
64 = 16 + AD²
AD² = 64 - 16
AD² = 48
Taking square root,
AD = √48
= √16×3
= 4√3
Therefore, the altitude of the triangle is 4√3 cm
✦ Try This: Find the altitude of an equilateral triangle of side 9 cm
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.3 Problem 6
Find the altitude of an equilateral triangle of side 8 cm
Summary:
The altitude of an equilateral triangle of side 8 cm is 4√3 cm.
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