Question

$A$ took $15$ seconds to cross a rectangular field diagonally walking at the rate of $52$ m/min and B took the same time to cross the same field along its sides, walking at the rate of $68$ m/min. The area of the field is:

• A. $30m^2$
• B. $40m^2$
• C. $50m^2$
• D. $60m^2$

Answer 1

Answer: (D)

$60m^2$

Distance covered by A in 15 $l=52\times \frac{15}{60}=13m$
therefore, length of diagonal$=13m$
Distance traveled by B in 15 $l=68\times \frac{15}{60}=17m$
therefore, $l+b=17m⟶\left(1\right)b=13m\sqrt{l^2+b^2}=13l^2+b^2=169⟶\left(2\right)$
from(1), $l+b=17m$
squaring, ${(l+b)}^2={\left(17\right)}^2{l}^2+b^2+2lb=289$
from (2), put $(l^2+b^2),169+2lb=2892lb=120lb=60c{m}^2$
$\therefore$ Area of the field$=60m^2$