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Question

If ABC is an equilateral triangle of side a, prove that its altitude =32a [3 MARKS]

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Solution

Concept: 1 Mark
Application: 1 Mark
Proof : 1 Mark

ΔABC is an equilateral triangle.

We are given that AB = BC = CA = a. AD is the altitude, i.e., ADBC.

Now, in right angled triangles ABD and ACD, we have

AB=AC [Given]

and AD=AD [Common side]

ΔABDΔACD [By RHS congruence]

BD=CD [ C.P.C.T]

BD=12BC=a2

From right triangle ABD,

AB2=AD2+BD2

a2=AD2+(a2)2

AD2=a2a24=34a2

AD=3a2


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