Question

A square has a perimeter of 20cm if each side had its length doubled what is the new area?

Answer 1

Step-by-step explanation:

Question :-

A square has a perimeter of 20cm if each side had its length doubled what is the new area?

Solution:-

Find It

what is the new area?

Given:-

A square has a perimeter of 20cm if each side

According to the Question

Let be the length and be the breadth.

GIVEN,

$\bf \: length \times breadth \: = 20$

When both of doubled.

$\bf \: l = 2l \\ \bf \: b = 2b$

where l' and b' are the increased sides

Formula

$\bf \: new \: area \: = l \times b$

according to the Question

each side had its length doubled

$\bf \: 2l \times 2b = 4(l \times b) \\ \bf \red{ 4 \times 20 = 80 {cm}^{2} }$

Hence

$\bf \: The \: new \: Area \: Is \: \red{ 80 {cm}^{2} }$

Answer 2

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

A square has a perimeter of 20cm if each side had its length doubled what is the new area ?

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{Given}}}}$

• perimeter of square = 20 cm

$\Large{\underline{\mathfrak{\bf{condition}}}}$

• each side of square be double

$\Large{\underline{\mathfrak{\bf{Find}}}}$

• Area of new square .

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

Let,

• side of square = x cm

Then,

$\boxed{\underline{\sf{\orange{\:perimeter_{square}\:=\:4\times(sides)}}}}$

keep value of side and perimeter,

$:\mapsto\sf{\:20\:=\:4\times x} \\ \\ \\ :\mapsto\sf{\:(x)\:=\:\dfrac{20}{4}} \\ \\ \\ :\mapsto\sf{\red{\:x\:=\:5\:cm}}$

Condition A/C to question,

( each side of square be double )

• side will be x = 2x = 2 × 5 = 10 cm

So,

$\boxed{\sf{\underline{\red{\:Area_{new\:square}\:=\:(side)^2}}}}$

Keep value of side,

$:\mapsto\sf{\:Area_{new\:square}\:=\:(10)^2} \\ \\ \\ :\mapsto\sf{\:Area_{new\:square}\:=\:10\times 10} \\ \\ \\ :\mapsto\sf{\blue{\:Area_{new\:square}\:=\:100\:cm^2}}$

$\Large{\underline{\mathfrak{\bf{Hence}}}}$

• Area of new square be = 100 cm²

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