Question

kiran and mai are standing at one corner of a rectangular field of grass looking at the diagonally opposite corner. kiran says that if the field were twice as long and twice as wide, then it would be twice the distance to the far corner. mai says that it would be more than twice as far, since the diagonal is even longer than the side lengths. complete the statement about whether you agree with either of them. i agree with select choice select choice (lesson 14) kiran mai both of them neither of them

Explanation:

Step1: Let the length of the rectangle be $l$ and the width be $w$.

The length of the diagonal $d$ of the original rectangle is given by the Pythagorean theorem: $d = \sqrt{l^{2}+w^{2}}$.

Step2: If the length and width are doubled, the new length is $2l$ and the new width is $2w$.

The new diagonal $d_{new}$ is $d_{new}=\sqrt{(2l)^{2}+(2w)^{2}}=\sqrt{4l^{2} + 4w^{2}}$.

Step3: Simplify the new - diagonal expression.

$d_{new}=\sqrt{4(l^{2}+w^{2})}=2\sqrt{l^{2}+w^{2}} = 2d$.

Answer:

neither of them