Question

A square lawn is surrounded
by a hath 2m wide of the
area of the hatha is 240 m²
find the area of the lawn.​

Answer 1

Sølution :

• Let the side of the lawn be " x "

• Then area of square lawn be " x² "

• Length of outer square = ( x + 4 ) m

• Area of outer square = ( x + 4 )² m²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= x² + 4² + 2(x)(4) m²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= x² + 8x + 16 m²

☯ Area of path will be :

= Area of outer square - Area of lawn

⇒240 = x² + 8x + 16 - x²

⇒240 = 8x + 16

⇒8x = 240 - 16

⇒8x = 224

⇒x = $\sf \dfrac{224}{8}$

⇒x = 28 m

• Then side of lawn :

= x + 2 = 28 + 2 = 30 m

• Area of lawn

= 28 × 28 = 784 m²

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