Question

solve this for me
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Answer 1

★Question :-

• If each side of a triangle is doubled then find the ratio of area of triangle thus formed and the given Triangle. Also find the percentage increase in area?

★Answer :-

• Area will become 4 times

• 300 %

★Solution :-

• Let us Consider an triangle with all sides equal ( Side = a )

• Area of triangle when its sides is a :-

$\sf{\boxed{\green{Area(\ A_{1})= \dfrac{\sqrt{3}\ a^{2}}{4}}}}$

• Area of triangle when its sides is doubled:-

$\sf{Area(\ A_{2})= \dfrac{\sqrt{3}\ (2a)^{2}}{4}}$

$\sf{Area(\ A_{2})= \dfrac{\sqrt{3}\times 4\ a^{2}}{4}}$

$\sf{Area(\ A_{2})= \dfrac{\sqrt{3}\times \cancel{4}\ a^{2}}{\cancel{4}}}$

$\sf{\boxed{\green{Area(\ A_{2})= \sqrt{3}a^{2}}}}$

• Now Compare $\sf\ A_{1} and \ A_{2}$

$\bf\huge{\boxed{\boxed{\dag{\ A_{2}= 4\ A_{1}}}}}$

Increased Percentage :-

$\implies{\dfrac{3A}{A}\times 100}$

$\implies{\dfrac{3\cancel{A}}{\cancel{A}}\times 100}$

$\implies{3\times 100}$

$\implies{300}$%

So, the Area of the triangle is increased by 300%

Answer 2

Area will become 4 times

300 %

$\purple{\boxed{\boxed{\boxed{solution:-}}}}$

Let us Consider an triangle with all sides equal ( Side = a )

• Area of triangle when its sides is a :-

\sf{\boxed{\green{Area(\ A_{1})= \dfrac{\sqrt{3}\ a^{2}}{4}}}}

Area( A

1 )= 4

3 a2

• Area of triangle when its sides is doubled:-

\sf{Area(\ A_{2})= \dfrac{\sqrt{3}\ (2a)^{2}}{4}}Area( A

2 )= 43

(2a) 2

\sf{Area(\ A_{2})= \dfrac{\sqrt{3}\times 4\ a^{2}}{4}}Area( A

2 )= 43 ×4 a 2

\sf{Area(\ A_{2})= \dfrac{\sqrt{3}\times \cancel{4}\ a^{2}}{\cancel{4}}}Area( A

2 )= 4

3 × 4

a 2

\sf{\boxed{\green{Area(\ A_{2})= \sqrt{3}a^{2}}}}

Area( A

2 )= 3

a 2

Now Compare \sf\ A_{1} and \ A_{2} A

1

and A

2

\bf\huge{\boxed{\boxed{\dag{\ A_{2}= 4\ A_{1}}}}}

† A

2) =4 A 1

Increased Percentage :-

\implies{\dfrac{3A}{A}\times 100}⟹

A

3A ×100

\implies{\dfrac{3\cancel{A}}{\cancel{A}}\times 100}⟹

A

3 A ×100

\implies{3\times 100}⟹3×100

\implies{300}⟹300 %

So, the Area of the triangle is increased by 300%