Question

The length of the altitude of an equilateral triangle with side 10√3 cm is ....... ​

Answer 1

GIVEN:

• Side of an equilateral triangle = 10√3 cm

TO FIND:

• What is the height of an equilateral triangle ?

SOLUTION:

We have given the side of an equilateral triangle is 10√3 cm

To find the height of an equilateral triangle, we use the formula:-

❰ HEIGHT = $\bf{\dfrac{\sqrt{3}}{2}}$$\times$ Side ❱

According to question:-

On putting the given values in the formula, we get

➠ H = $\sf{\dfrac{\sqrt{3}}{2}}$$\times$ 10$\sf{\sqrt{3}}$

➠ H = $\sf{\dfrac{3 \times 10}{2}}$

➠ H = $\sf{\cancel\dfrac{30}{2}}$

❮ HEIGHT = 15 cm ❯

❝ Hence, the height of an equilateral triangle is 15 cm ❞

______________________

Answer 2

Given:-

• The side of an Equilateral triangle = 10√3.

To Find:-

• The height of the Equilateral triangle.

Solution:-

We know,

The formula of height of the Equilateral triangle.

$\rm{ \: Height \: = \sqrt{ \frac{3}{2} } \times Side}$

Now, by putting the value,we get,

$\rm{Height = \sqrt{ \frac{3}{2} } \times 10 \sqrt{3} }$

$\rm{Height \: = \frac{3 \times 10}{2}}$

$\rm{Height = \cancel\frac{30}{2} }$

$\rm{Height = 15 \: cm}$

Hence, the length of the altitude of an equilateral triangle with side 10√3 cm is 15 cm.