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The altitude of an equilateral triangle …

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The altitude of an equilateral triangle is 3 root 3. Find its area.

Posted by Ansh Sharma 8 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Hans Raj 8 years, 5 months ago

let ABC is a an equilateral triangle with side AB=BC=CA= X

and AD = altitude = 3 root 3

AD is perpendicular to BC and BD=DC=X/2

Also ABD is a right Ld triangle with AB=X , BD=X/2 , AD= 3 root 3

AB2 = BD2 + AD2

X2 = (X/2)2 + (3ROOT3)2

3/4 X2= 9X3

X2=36

X=6

AREA=1/2 X BASE X HEIGHT

= 1/2 x BC x AD

= 1/2 x Xx 3root3

= 1/2 x 6 x 3root3

= 9 root3 cm2

Check ur answer by HERON'S RULE s=6+6+6/2 = 9 , area = root 9(9-6)(9-6)(9-6) = root 9x3x3x3 = 9root3 ok r u happy

1Thank You

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