Question

Calculate the height of an equilateral triangle each of whose sides measures 12 cm.

Answer 1

Area of the triangle = √3/4√ a² square units

= √3/4 × 12 × 12

= 36√3 cm²

= 36 × 1.732 cm²

= 62.28 cm

The height is AB² = AD² + BD²

12² = AD² + 6²

144 = AD² + 36

144 − 36 = AD²

AD² = 108

AD = √108  

AD = 10.39 cm

Answer 2

SOLUTION :  

GIVEN : Side of an equilateral ∆ = 12 cm

Let ∆ABC is an equilateral ∆ with  AB = BC = AC = 12 cm and Draw AD ⊥ BC .

In ∆ABD and ∆ACD

∠ADB = ∠ADC           [Each 90°]

AB = AC            [given]

AD = AD           [Common]

∆ABD ≅ ∆ACD     [By RHS condition]

BD = CD         [By c.p.c.t]

Therefore , BD = CD= 6 cm

In ∆ ABD ,  

AB² = AD² + BD²

12² = AD² + 6²

144 = AD² + 36

144 − 36 = AD²

AD² = 108

AD = √108  

AD = 10.39 cm

Hence, the height of the equilateral triangle is 10.39 cm.

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