If the diagonal of a square is changing at the rate of 0.5 cm s -1. Then the rate of change of area, when the area is 400 cm 2, is

Question

If the diagonal of a square is changing at the rate of 0.5 cm s -1. Then the rate of change of area, when the area is 400 cm 2, is (A) 20 √2 cm 2 / s (B) 10 √2 cm 2 / s (C) (1/10 √2) cm 2 / s (D) (10/√2) cm 2 / s

Tardigrade Admin · Accepted Answer

text Let square of side = a ∴ text diagonal = a √2 √2 ( da / dt )=0.5 text and a 2=400 ⇒ a =20 ∴ A = a 2 ⇒ ( dA / dt )=2 a ( da / dt ) ( dA / dt )=2 × 20 × (1/2 √2)=10 √2 cm 2 / s

Q. If the diagonal of a square is changing at the rate of $0.5 c m s^{- 1}$ . Then the rate of change of area, when the area is $400 c m^{2}$ , is

$202 c m^{2} / s$

$102 c m^{2} / s$

$\frac{1}{10 2} c m^{2} / s$

$\frac{10}{2} c m^{2} / s$

$Let square of side = a$
$∴ diagonal = a 2$
$2 \frac{d a}{d t} = 0.5 and a^{2} = 400 \Rightarrow a = 20$
$∴ A = a^{2} \Rightarrow \frac{d A}{d t} = 2 a \frac{d a}{d t}$
$\frac{d A}{d t} = 2 \times 20 \times \frac{1}{2 2} = 102 c m^{2} / s$

Q. If the diagonal of a square is changing at the rate of 0.5cms−1. Then the rate of change of area, when the area is 400cm2, is

202​cm2/s

102​cm2/s

102​1​cm2/s

2​10​cm2/s