A wire when bent in the form of an equilateral triangle encloses an area of 64 -3 cm2- Then- find the area enclosed by the same wire when bent to form a square-

You visited us 63 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Triangle as Part of Rectangle

A wire when b...

Question

A wire when bent in the form of an equilateral triangle encloses an area of $64 \sqrt{3} c m^{2} .$ Then, find the area enclosed by the same wire when bent to form a square.

Open in App

Solution

Let the side of the equilateral $Δ l e$ 'a' and the side of the square be 'x' we know, area of equilateral $Δ = \frac{\sqrt{3}}{4} a^{2}$

$64 \sqrt{3} = \frac{\sqrt{3}}{4} a^{2}$

$∴ a^{2} = 8^{2} \times 2^{2}$

$a = 16 c m$

Perimeter of equilateral $Δ = 3 (16)$

= 48 cm

Hence, perimeter of square = 48 cm

i.e., $4 \times = 48 \Rightarrow x = 12 c m$

Area of square $= x^{2}$

$= (12)^{2}$

$= 144$

Suggest Corrections

Similar questions

Q. A wire when bent in the form of a square encloses an area of

484 m^{2}

. Find the largest area enclosed by the same wire when bent to form an equilateral triangle.

A wire when bent in the form of an equilateral triangle encloses an area of $64 \sqrt{3} c m^{2} .$ The area enclosed by the same wire when bent to form a square is ___ $c m^{2}$

A wire when bent in the form of a square encloses an area =

576 c m^{2}

. Find the largest area enclosed by the same wire when bent to form an equilateral triangles.

Q. A wire when bent in the form of a square encloses an area of 484

m^{2}

. Find the largest area enclosed by the same wire when bent to form:
(i) an equilateral triangle.
(ii) a rectangle of breadth 16 m.

Q. A wire when bent in the form of an equilateral triangle encloses an area of

121 \sqrt{3} {cm}^{2}

. The same wire is bent to form a circle. Find the area enclosed by the circle.

Join BYJU'S Learning Program

A wire when bent in the form of an equilateral triangle encloses an area of 64√3 cm2. Then, find the area enclosed by the same wire when bent to form a square.

Let the side of the equilateral Δle 'a' and the side of the square be 'x' we know, area of equilateral Δ=√34a2 64√3=√34a2 ∴a2=82×22 a=16 cm Perimeter of equilateral Δ=3(16) = 48 cm Hence, perimeter of square = 48 cm i.e., 4×=48⇒x=12 cm Area of square =x2 =(12)2 =144

A wire when bent in the form of an equilateral triangle encloses an area of $64 \sqrt{3} c m^{2} .$ Then, find the area enclosed by the same wire when bent to form a square.