Question

find the length of the alltitude of an equilateral triangle whose each side is 8 cm​

Answer 1

• The altitude of an equilateral triangle whose side is 8 cm is 4√3 cm.

Given:

Each side of an equilateral triangle is 8 cm.

To find:

The length of the altitude of the equilateral triangle.

Something about an equilateral triangle,

• The triangle has three equal sides.
• All the interior angles are 60° each.
• The perpendicular side to a side divides that side equally.

So, from the image(attached)

We can get that,

ABC is an equilateral triangle,

• AB = BC = AC = 8 cm each.
• AD is perpendicular to BC (drawn)
• So, we have BD = CD = 8/2 = 4 cm each.
• As AD⊥BC, ΔADB and ΔADC are two right-angled triangles right-angled at ∠ADB and ∠ADC respectively.

Using Pythagoras Theorem, in a triangle ADB

⇒ (AD)² + (BD)² = (AB)²

⇒ (AD)² + (4)² = (8)²

⇒ (AD)² + 16 = 64

⇒ (AD)² = 64 - 16

⇒ (AD)² = 48

⇒ AD = √48

∴ AD = 4√3 cm

Answer 2

Answer:

✡ Given ✡

$\leadsto$ An equilateral triangle whose each side is 8 cm.

✡ To Find ✡

$\leadsto$ What is the length of the altitude of an equilateral triangle.

✡ Solution ✡

➡ BD = CD = $\dfrac{1}{2}$BC = $\dfrac{8}{2}$ = 4 cm

Now, AB² = AD² + BD² [$\mapsto$ By Pythagoras Theorem]

$\implies$ (8)² = AD² + (4)²

$\implies$ 64 = AD² + 16

$\implies$ AD² = 64 - 16 = 48

$\implies$ AD = $\sqrt{48}$

$\implies$ 4$\sqrt{3}$ cm

$\therefore$ Altitude of an equilateral triangle is 4$\sqrt{3}$ cm

Step-by-step explanation:

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