The height of an equilateral triangle is
$\frac{\sqrt{3}}{4} \times S i d e$
$\frac{\sqrt{3}}{2} \times S i d e$
$\frac{\sqrt{3}}{4} \times S i d e^{2}$
None of these

Question

The height of an equilateral triangle isdisplaystyle dfrac-sqrt-3-4-times Side displaystyle dfrac-sqrt-3-2-times Side displaystyle dfrac-sqrt-3-4-times Side-2- None of these

Toppr Admin · Accepted Answer

In-xA0-x394-ABD-AD-2-AB-2-x2212-BD-2-xA0-a-2-x2212-a2-2-a2-x2212-a24AD2-3a24-x2234-AD-x221A-3a2-x2234- Height of an equilateral triangle is-xA0-x221A-32-xD7-side

The height of an equilateral triangle is√34×Side√32×Side√34×Side2None of these

In ΔABD,(AD)2=(AB)2−(BD)2= (a)2−(a2)2=a2−a24AD2=3a24∴AD=√3a2∴ Height of an equilateral triangle is √32×side

The height of an equilateral triangle is
$\frac{\sqrt{3}}{4} \times S i d e$
$\frac{\sqrt{3}}{2} \times S i d e$
$\frac{\sqrt{3}}{4} \times S i d e^{2}$
None of these

In $Δ A B D$ ,
${(A D)}^{2} = {(A B)}^{2} - {(B D)}^{2}$ = ${(a)}^{2} - {(\frac{a}{2})}^{2} = a^{2} - \frac{a^{2}}{4}$

$A D^{2} = \frac{3 a^{2}}{4}$

$∴ A D = \frac{\sqrt{3} a}{2}$
$∴$ Height of an equilateral triangle is $\frac{\sqrt{3}}{2} \times s i d e$