Kylie needs to pack her baton for a

color-guard competition. The baton

is 38 inches long. She has a rectangular

box with a base of 13 inches by 35

inches and a height of 13 inches.

Part A

Could the baton lie flat on a diagonal

along the base of the box? Explain.

Part B

Could the baton fit along the interior

diagonal of the box? Explain.

Step-by-step explanation:

For A, we would need to use the Pythagorean theorem. We have 13^2+35^2=38^2. Is this true? No It is not, 13^2 + 35^2 = 1394. The square root of that is about 37.3, so it does not fit.

For B, we would need to use the Pythagorean theorem again, but in a different way. We would need to find 13^2 + 35^2, and then square root that. That would be our base of our right triangle. The height would be 13, and we use the Pythagorean theorem again! We get 169+1394=1563. The square root of 1563 is about 39.5, so it does fit.