Question

each side of an equilateral triangle is 10cm long. The height of the triangle is?​

Answer 1

$\bigstar$ Question:

• If each side of an equilateral triangle is 10cm, then what is the height of the triangle?

$\bigstar$ To find:

• The length of the height.

$\bigstar$ Solution:

$\star$ How to find?

• First of all, you have to find the area of the equilateral triangle with the help of the formula for it, i.e.

$\frac{ \sqrt{3} }{4 } {a}^{2}$

• Then, you can equate the area with the formula of a triangle,
• $\frac{1}{2} \times height \times base$
• After that, you will get the value of the height.

$\star$Process:

• Side of the equilateral triangle = 10cm
• Formula for finding the area of an equilateral triangle

$\frac{ \sqrt{3} }{4} {a}^{2}$

where ' a ' is the side of the equilateral triangle.

So, by putting it's value, we get,

$\frac{ \sqrt{3} }{4} {a}^{2} \\ = \frac{ \sqrt{3} }{4} \times {10}^{2} \\ = \frac{ \sqrt{3} }{4} \times 10 \times 10 \\ = \frac{ \sqrt{3} \times 100 }{4} \\ = \sqrt{3} \times 25 \\ = 25 \sqrt{3}$

• Therefore, the area of the equilateral triangle = 25√3 cm²
• Now, by equating it's area with the formula that is for finding the area of any triangle, we get,

$25 \sqrt{3} = \frac{1}{2} \times height \times base$

$\implies$ 25√3 = 1/2 × h × 10

$\implies$ 25√3 = 5h

$\implies$ h = (25√3)/5

$\implies$ h = 5√3 cm.

$\bigstar$Answer:

• Therefore the height of the equilateral triangle is 5√3 cm.

Answer 2

Answer:

Height of equilateral triangle is 5√3 cm .

Step-by-step explanation:

Given :- Problem statement :

• length of the side of equilateral triangle = 10 cm

To find :- height of triangle .

Solution :-

Step 1) Let the triangle be ΔABC .

$l(AB) = l(BC) = l(AC) = 10 cm$

Step 2) Let the height of triangle be h cm ,

Step 3) We know the formula for height of equilateral triangle is

  $h = \frac{\sqrt{3} }{2} * (side)$ -- (1)

Therefore , $h = \frac{\sqrt{3} }{2}* 10 \\ h = 5\sqrt{3}$

Hence , height of equilateral triangle is 5√3 cm .

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