Question

AREA OF AN EQUILATERAL TRIANGLE IS 25 ROOT 3CM SQUARE. FIND THE PERIMETER OF THE TRIANGLE

Answer 1

Answer:

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Answer 2

Gɪᴠᴇɴ

Area of equilateral triangle = 25√3 cm²

Tᴏ ꜰɪɴᴅ

Perimeter of triangle

Sᴏʟᴜᴛɪᴏɴ

As we know the formula :

⇒ Area of equilateral ∆ = √3(a²)/4 unit²

Pᴜᴛᴛɪɴɢ ᴠᴀʟᴜᴇꜱ ᴡᴇ ɢᴇᴛ :

⇒ 25√3 = √3a²/4

⇒ 25√3 × 4 = √3a²

⇒ 100√3 = √3a²

⇒ a² = 100√3/√3

⇒ a² = 100

⇒ a = √100

⇒ a = 10 cm

Now we know that,

⇾ Perimeter of ∆ = Sum of 3 sides

⇾ Sides of equilateral ∆ are equal

Let the three sides be a, b & c & a = b = c

Pᴜᴛᴛɪɴɢ ᴠᴀʟᴜᴇꜱ ᴡᴇ ɢᴇᴛ :

⇒ Perimeter = a + b + c

⇒ Perimeter = a + a + a

⇒ Perimeter = 3a

⇒ Perimeter = 3(10)

⇒ Perimeter = 30 cm

Tʜᴇʀᴇꜰᴏʀᴇ,

Perimeter of equilateral triangle = 30cm