Question

Rolly has a equilateral triangular frame of wire having area of cross-section 64 √3 cm. She wanted to change this frame into circular frame. She wanted to know then what will be the radius of circular frame.​

Answer 1

Given :- Rolly has a equilateral triangular frame of wire having area of cross-section 64 √3 cm.

To Find :- The radius of circular frame ?

Formula used :-

• Area of equilateral triangle = (√3/4) × (side)² .
• Perimeter of equilateral triangle = 3 × side .
• Circumference of circle = 2 × π × radius .

Solution :-

Let side of equilateral triangular frame is a cm .

So,

→ (√3/4)a² = 64√3

→ a² = 64 × 4

→ a² = 8² × 2²

→ a² = (8 × 2)²

→ a² = 16²

→ a = 16 cm

then,

→ Perimeter of equilateral triangular frame = 3 × 16 = 48 cm

now,

→ circumference of circular frame = 48 cm

→ 2 × π × radius = 48

→ π × radius = 24

→ 3.14 × radius = 24

→ radius = 24/3.14

→ radius ≈ 7.64 cm (Ans.)

Hence, the radius of circular frame is equal to 7.64 cm .

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Answer 2

Answer:

84/11

Step-by-step explanation:

Area of triangle = root3/4×side² 64root3 = roo3/4 × side² 64root3×4/root3 = side²

256=side²

side=root256=16cm

perimeter of triangle =3side

= 48cm

Circumference =2pi r

48cm=2×22/7 ×r

48×7/44=r

r= 84/11cm