Question

10. Find the perimeter and area of an equilateral triangle whose height is 12 cm. Write your
answers, correct to two decimal places.​

Answer 1

$\blue{\bold{\underline{\underline{Given}}}}$

• Height (h) of an equilateral triangle = 12 cm

$\blue{\bold{\underline{\underline{To Find}}}}$

• Perimeter of Eq. Triangle

• Area of Eq. Triangle

$\blue{\bold{\underline{\underline{Solution}}}}$

We know that,

➦ Height (h) of Eq. Triangle = √3a/2 ,

where, a = side of Eq. Triangle

Now,

→ 12 = √3a/2

→ 12×2 = √3a

→ 24 = √3a

→ a = 24/√3. --(1)

Use √3 = 1.73 , We get,

→ a = 24/1.73

→ a = 13.87 ≈ 13.90 m

Now,

We know that,

➦ Perimeter of Equilateral triangle = 3a

➠ 3a = 3 × 13.9 = 41.7 m

➦ Area of Equilateral triangle = √3a²/4

→ √3 × (24/√3)² / 4. ---from(1)

→ √3 × 576/3 / 4

→ √3 × 192/4

→ √3 × 48

→ 1.73 × 48

→ 83.04 m²

Hence,

• Pᴇʀɪᴍᴇᴛᴇʀ = 41.70 m

• ᴀʀᴇᴀ = 83.04 m²

Answer 2

Perimeter = 41.70m

Area = 83. 04m^2

Explanation:

Given,

Height = 12 cm

We know that,

Height (h) of Eq.Triangle = √3a/2

Where,

a= side of eq.Triangle

Now,

$12 = \frac{ \sqrt{3a} }{2}$

12×2 =√3a

24 = √3a

a=24/√4 ----> 1⃣

we know that

√3=1.73

a=24/1.73

a=13.90m

Now,

perimeter of a eq. Triangle = 3a

3a = 3×13.90

=41.7m

Area of eq. Triangle = √3 a^2/4

$\sqrt{3} \times { \frac{24}{ \sqrt{3} } }^{2} \frac{4}{?}$

$\frac{ \sqrt{3} \times \frac{576}{3} }{4}$

$\frac{ \sqrt{3} \times 192 }{4}$

√3×48

1.73×48

${83.04m}^{2}$