Question

the area of the square is hundred square centimetre of the sides aap per square increase 10% then what is area and perimeter ​

Answer 1

Given

Area of square = 100 cm²

Side of square increases by 10%

To find

New perimeter & area of square.

Solution

Here, area of original square = 100 cm²

We know that,

➥ Area of square = Side²

➝ 100 = Side²

➝ Side = √100

➝ Side = 10 cm.

Now finding new side of square :

➪ New side = 10 + (10% of 10)

➪ New side = 10 + (1/10 of 10)

➪ New side = 10 + 1

➪ New side = 11 cm.

Now finding new area of square :

➼ New area = New side²

➼ New area = 11²

➼ New area = 121 cm²

Now finding new perimeter of square :

➺ New perimeter = 4 × New side

➺ New perimeter = 4 × 11

➺ New perimeter = 44 cm.

Hence,

Area of new square is 121 cm² & new perimeter of square is 44 cm.

Answer 2

Aɴꜱᴡᴇʀ

✪ $\large \rm{area \: - \: 121 \: c {m}^{2} }$

✪ $\large \rm{}perimter \: - \: \: 44 \: cm$

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Gɪᴠᴇɴ

★ Area of the square - 100 cm²

★ The side of the square is being increase by 10%

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ᴛᴏ ꜰɪɴᴅ

The area and the perimeter of the new square.

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Sᴛᴇᴘꜱ

The area of a square is given by Side²

$\tt \leadsto{}sid {e}^{2} = 100 \\ \\ \tt \leadsto{}side = \sqrt{100 } \\ \\ \tt \leadsto{ \red{side = 10 \: cm}}$

➜ So if the side was increased by 10% then the size of the new side would be,

$\tt \mapsto{}10 + \cancel{ \frac{10}{100} }\times { 10} \\ \\ \tt \mapsto10 + 1 \\ \\ \tt \mapsto{ \orange{11 \: cm}}$

☞ So now we can just use our usual formula to find area of the new square, that is Side²

$\tt{} \hookrightarrow{} {11}^{2} \\ \\ \tt {\pink{ \hookrightarrow{}121 \: c {m}^{2} }}$

➠ And the new perimeter of the square can be calculated with the use of 4a, that is

$\tt \dashrightarrow{}4 \times 11 \\ \\ \tt{ \purple{ \dashrightarrow44 \: cm}}$

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