If the sides of a square are decreasing at the rate of \( 1.5 cm / sec

1.	If the sides of a square are decreasing at the rate of \( 1.5 cm / sec \), at what rate is its area decreasing when its side is \( 8 cm \) ?
Answer» lengthofsquare×4=perimeter hancerateofchangeofperimeter 1.5×4=6 unit is cm/sec Let side of square be a cm. Given that \(\frac{da}{dt} = -1.5 cm/sec\) \(\because A = a^2\) ⇒ \(\frac{da}{dt}= 2a\frac{da}{dt} = -3a\, cm^2/sec\) ⇒ \(\left[\frac{dA}{dt}\right]\, \text{at} \,a = 8cm = - 3 \times 8 = -24 cm^2/sec.\) Hence, area of square is decreasing at the rate of 24 cm²/ sec when its side is 8 cm.

If the sides of a square are decreasing at the rate of \( 1.5 cm / sec \), at what rate is its area decreasing when its side is \( 8 cm \) ?

Answer» lengthofsquare×4=perimeter

hancerateofchangeofperimeter

1.5×4=6

unit is cm/sec

Let side of square be a cm.

Given that \(\frac{da}{dt} = -1.5 cm/sec\)

\(\because A = a^2\)

⇒ \(\frac{da}{dt}= 2a\frac{da}{dt} = -3a\, cm^2/sec\)

⇒ \(\left[\frac{dA}{dt}\right]\, \text{at} \,a = 8cm = - 3 \times 8 = -24 cm^2/sec.\)

Hence, area of square is decreasing at the rate of 24 cm²/ sec when its side is 8 cm.

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If the sides of a square are decreasing at the rate of \( 1.5 cm / sec \), at what rate is its area decreasing when its side is \( 8 cm \) ?

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