Question

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If each side of a square is increased by 10%, find the increase percent in its area.​

Answer 1

Answer:

21%

Step-by-step explanation:

let the 10 cm side of square

now area of square =side × side

10×10 = 100 cm square

now 10% increase side of square

then ......

Answer 2

Answer:

★ Increase Percent = 21% ★

Step-by-step explanation:

Given:

• Each side of Square is increased by 10%

To Find:

• Total percentage change in area of square

Solution: Let the side of Square be x

★ Area of Square = ( Side )² = x² ★

A/q

• Side is increased by 10%

Therefore, New side = x + 10/100 of x

$\small\implies{\sf }$ x + 10x/100 [ Take LCM ]

$\small\implies{\sf }$ 100x + 10x/100

$\small\implies{\sf }$ 110x/100

$\small\implies{\sf }$ 11x/10

∴ New area of square = ( Side)²

$\small\implies{\sf }$ New area = (11x/10)²

$\small\implies{\sf }$ New area = 121x²/100

• Total increase in area = ( New area – Original area ) •

$\small\implies{\sf }$ Increase in area = 121x²/100 – x² [ Take LCM ]

$\small\implies{\sf }$ 121x² – 100x²/100

$\small\implies{\sf }$ 21x²/100

∴ Increase % in area = (Increased area/Original area) x 100

$\small\implies{\sf }$ Increase % = (21x²/100/x²)100

$\small\implies{\sf }$ Increase % = ( 21x²/100 (1/x²) ( 100 ) [ Cancel similar terms x² and 100 ]

$\small\implies{\sf }$ Increase % = 21%

Hence, The increase percent in area of square is 21%