Question

The area of a rectangular field is 48 metre square and one of its side is 6 m how long will a lady take to cross the field diagonally @ 20 m per minute

Answer 1

Answer:   30 secs.   

Step-by-step explanation:  Let ABCD be the rectangular field of area 48 metre square and let AB=CD=6 metre. So, BC=AD= 48/6=8 metre.

The lady is crossing the field diagonally, so she is walking along BD. Also, since every angle of a rectangle is 90°, so ΔABD is a right angled-triangle with BD as the hypotenuse.

Therefore, using Pythagoras theorem, we have

$BD^2=AB^2+AD^2\\\Rightarrow BD=\sqrt{AB^2+AD^2}=\sqrt{6^2+8^2}=10.$

Now, to cover 20 metre, the lady takes 1 min.

So, to cover 10 metre, the lady will take $\dfrac{1}{20}\times 10=\dfrac{1}{2}$min=30 secs.

Thereforere, the lady will take 30 seconds to cross the field diagonally.

Answer 2

Answer:

Let ABCD be the rectangular field of area 48 metre square and let AB=CD=6 metre. So, BC=AD= 48/6=8 metre.

The lady is crossing the field diagonally, so she is walking along BD. Also, since every angle of a rectangle is 90°, so ΔABD is a right angled-triangle with BD as the hypotenuse.

Therefore, using Pythagoras theorem, we have

\begin{gathered}BD^2=AB^2+AD^2\\\Rightarrow BD=\sqrt{AB^2+AD^2}=\sqrt{6^2+8^2}=10.\end{gathered}

BD

2

=AB

2

+AD

2

⇒BD=

AB

2

+AD

2

=

6

2

+8

2

=10.

Now, to cover 20 metre, the lady takes 1 min.

So, to cover 10 metre, the lady will take \dfrac{1}{20}\times 10=\dfrac{1}{2}

20

1

×10=

2

1

min=30 secs.

Thereforere, the lady will take 30 seconds to cross the field diagonally.