Question

Miranda is standing at the corner of a 7m by 11m field. She needs to go to the corner diagonally opposite from where she is standing. How much shorter is it if she cuts across the diagonal instead of walking around the perimeter of the field? Round your answer to the nearest hundredth of a meter.

Answer 1

We can use the Pythagorean Theorem to find the distance from one corner of the field to the corner opposite it diagonally and subtract it from the length from one corner to the other while walking around the perimeter. Walking around the edge to the other corner is
`11+6=\boxed{18}` meters. Using the Pythagorean Theorem to calculate the diagonal distance from one corner to the other, we get:

`\sqrt{7^(2)+11^(2)}`

`√(49+121)`

`√(170)`

`\approx \boxed{13.038}`.

Subtracting the two, we have our answer:
`18-13.038\approx\boxed{4.96}`.

So, our answer is 4.96 meters.

Answer 2

4.96 m

Explanation:

Use Pythagorean Theorem to solve for diagonal: 7^2 + 11^2 = c^2.

To get perimeter distance add 7 + 11.

Diagonal= 13.04 m

1/2 Perimeter= 18

Then subtract.