Question

if the area of an equilateral triangle is 15 root 3 cm square then find the length of its altitude​

Answer 1

Given that : Area of an equilateral triangle is 15√3 cm²

Need to find : Altitude of that triangle

Concept :

• Area of an equilateral triangle is :

      $\sf \dfrac{\sqrt{3}}{4} \times (side)^{2}$

• Height of an equilateral triangle is :

    $\sf \dfrac{\sqrt{3}}{2} \times ( side )$

           _________

Solution :

Finding the side -

$\sf : \; \implies \dfrac{\sqrt{3}}{4} \times (side)^{2} = 15\sqrt{3}$

$\sf : \; \implies \sqrt{3} \times (side)^{2} = 4 \times 15\sqrt{3}$

$\sf : \; \implies \sqrt{3} \times (side)^{2} = 60\sqrt{3}$

$\sf : \; \implies (side)^{2} = \dfrac{60\sqrt{3}}{\sqrt{3}}$

$\sf : \; \implies (side)^{2} = 60$

$\sf : \; \implies (side) = \sqrt{60}$

$\boxed{\bf{ Side = 2\sqrt{15}}} \; \bigstar$

           _________

Finding the Altitude -

$\sf : \; \implies Altitude = \dfrac{\sqrt{3}}{2} \times 2\sqrt{15}$

$\sf : \; \implies Altitude = \sqrt{3} \times \sqrt{15}$

$\sf : \; \implies Altitude = \sqrt{3 \times 3 \times 5}$

$\boxed{\bf{ Altitude = 3\sqrt{5}}} \; \bigstar$

           _________

• Henceforth, the length of altitude of that equilateral triangle is 3√5 cm.

Answer 2

Answer:

this is the answer of area of an equalateral triangle