Question

AROUND A SQUARE POOL ,

THERE IS A FOOTPATH OF WIDTH 2 M

IF THE AREA OF THE FOOTPATH IS
$\frac{5}{4}$
TIMES THAT OF THE POOL ,

FIND THE AREA OF THE POOL ...

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Answer 1

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your answer refers to the attachment!

Answer 2

Area of the footpath is 5/4 times the area of the pool .

Let the area of the pool be x² ( its side being x ) .

Then area of the footpath is 5 x² / 4 .

The width of the path is 2 m .

∴ Side of the big square = x + 2 + 2 = x + 4 m .

Area = ( x + 4 )² .

Area of square = area of pool + area of footpath .

⇒ ( x + 4 )² = x² + 5 x²/4

⇒ x² + 16 + 8 x = ( 4 x² + 5 x² )/4

⇒ 4 x² + 64 + 32 x = 9 x²

⇒ 5 x² - 32 x - 64 = 0

⇒ 5 x² - 40 x + 8 x - 64 = 0

⇒ 5 x ( x - 8 ) + 8 ( x - 8 ) = 0

x = 8 neglecting the negative value .

Area of pool = x²

⇒ 8²

⇒ 64 cm²

Area = 64 cm²