Question

Find the length of the height of an equilateral triangle of side 24 cm. (Take $\sqrt{3}$=1.73)

Answer 1

Let the height of the triangle be h cm.
Area of the triangle = $\left(\frac{1}{2}\times \mathrm{Base}\times \mathrm{Height}\right)$ sq. units
= $\left(\frac{1}{2}\times 24\times h\right)$ cm²

Let the side of the equilateral triangle be a cm.
Area of the equilateral triangle = $\left(\frac{\sqrt{3}}{4}{a}^2\right)$ sq. units
= $\left(\frac{\sqrt{3}}{4}\times 24\times 24\right)$ cm² = $\left(\sqrt{3}\times 144\right)$ cm²
∴ $\left(\frac{1}{2}\times 24\times h\right)$ = $\left(\sqrt{3}\times 144\right)$
⇒ 12 h = $\left(\sqrt{3}\times 144\right)$
⇒ h = $\left(\frac{\sqrt{3}\times 144}{12}\right)=\left(\sqrt{3}\times 12\right)=\left(1.73\times 12\right)=20.76$ cm
∴ Height of the equilateral triangle = 20.76 cm