Question

a wire in the shape of a equilateral triangle of side 12cm is reshaped to form a square.the side of the square in cm is __..
option
a)18
b)12
c)16
d)9
​

Answer 1

✩ Option ( c ) = 9 cm ☆

E x P l a n a t i o n :

Given:

• A wire in the shape of an equilateral triangle of the side is 12 cm is reshaped to form a square.

To find:

• The Side of Square$?$

Solution: The equilateral triangle is reshaped in the form of a square. & ∆ Side is 12 cm.

As We know that,

★ Perimeter of ∆ = 3 × (Side) ★

★ Perimeter of Square = 4 × (Side) ★

» Perimeter of ∆ :

⇥ Perimeter = 3 × 12

⇥ Perimeter = 36 cm

∴ Hence, Perimeter of the triangle is 36 cm.

A/q,

• The wire which was in the shape of an equilateral triangle is reshaped in the form of a square.

[Peri. of Square = Peri. of Equilateral Triangle]

➟ 4 × Side = 36

➟ Side = 36/4

➟ Side = 9 cm

∴ Hence, the side of the square is 9 cm.

Answer 2

Answer:

Given :-

• A wire in the shape of a equilateral triangle of side 12 cm is reshaped to form a square.

To Find :-

• What is the side of the square in cm.

Solution :-

First, we have to find the perimeter of a triangle :

As we know that :

$\clubsuit$ Perimeter Of Triangle Of Formula :

$\footnotesize\bigstar\: \: \sf\boxed{\bold{\pink{Perimeter_{(Equilateral\: Triangle)} =\: 3 \times Side}}}\: \: \bigstar$

Given :

• Side Of Triangle = 12 cm

According to the question by using the formula we get,

$\implies \sf Perimeter_{(Equilateral\: Triangle)} =\: 3 \times 12$

$\implies \sf\bold{\purple{Perimeter_{(Equilateral\: Triangle)} =\: 36\: cm}}$

Now, we have to find the side of the square :

As we know that :

$\clubsuit$ Perimeter Of Square Formula :

$\footnotesize\bigstar\: \: \sf\boxed{\bold{\pink{Perimeter_{(Square)} =\: 4 \times Side}}}\: \: \bigstar$

Let,

$\mapsto \bf Side_{(Square)} =\: a\: cm$

According to the question by using the formula we get,

$\bigstar$ The wire in the shape of a equilateral triangle of side 12 cm is reshaped to form a square.

$\footnotesize\: \leadsto \sf\bold{\blue{Perimeter_{(Square)} =\: Perimeter_{(Equilateral\: Triangle)}}}$

$\implies \sf 36 =\: 4 \times a$

$\implies \sf \dfrac{\cancel{36}}{\cancel{4}} =\: a$

$\implies \sf \dfrac{9}{1} =\: a$

$\implies \sf 9 =\: a$

$\implies \sf\bold{\red{a =\: 9\: cm}}$

${\small{\bold{\underline{\therefore\: The\: side\: of\: the\: square\: is\: 9\: cm\: .}}}}$

Hence, the correct options is option no d) 9 cm .

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★ VERIFICATION ★

$\leadsto \sf 36 =\: 4 \times a$

By putting a = 9 we get,

$\leadsto \sf 36 =\: 4 \times 9$

$\leadsto \sf\bold{\green{36 =\: 36}}$

Hence, Verified.