Question

Will ran the diagonal distance across a square field measuring 40 yards on each side. James ran the diagonal distance across a rectangular field with a length of 25 yards and a width of 35 yards. Who ran a longer distance, and how much longer did he run? Show work to prove your answer

Answer 1

Will ran the longest

He ran for 56.57 yards, 13.56 yards longer than James.

Step-by-step explanation:

Step 1 :

Will ran the diagonal across a square field measuring 40 yards in each side.

The diagonal of a square can be obtained by the square root of the sum of the squares of its 2 sides [Because it forms the hypotenuse of a right angle triangle]

Hence when the side is 40 yards , the diagonal would be

$\sqrt{40^{2} + 40^{2}} = \sqrt{1600 + 1600} = \sqrt{3200} =56.57 yards$

So Will ran for 56.57 yards

Step 2 :

James ran the diagonal of a rectangular field with 25 yards length and 35 yards width.

The diagonal of the rectangle can be obtained by the square root of the sum of squares of its length and width.

Hence when the length is 25 yards and width is 35 , the diagonal would be

$\sqrt{35^{2} + 25^{2}} = \sqrt{1225 + 625}} = \sqrt{1850} = 43.01$ yards

So James ran for 43.01 yards

Step 3 :

Will ran for 56.57 yards and 43.01 yards.

Hence Will ran for longer distance of 56.57 yards, which is 13.56 yards more than James.