Reggie has a rectangular piece of paper that is 12 inches long and 7 inches wide. he is going to cut the paper from corner to corner, along the diagonal. how many inches will reggie be cutting? if necessary, round to two decimal places.

A property from geometry states that rectangles have congruent opposite sides. Thus, no matter which diagonal Reggie cuts, it still has the same lengths. Since it's a rectangle and we cut from corner to corner, we create a right triangle. See the picture below:

12 inches

7 |

i |

n |

Because it's a rectangle, it won't matter which corner we cut. But if we fold at the cut lines, we would make an in the rectangle's center.

The cut line and two sides make a right triangle. One leg is 12, one leg is 7, and we need to find the third side. The Pythagorean Theorem - sum of the squares of the legs equals the square of the hypotenuse - is applied.

Let S = the length of the side from corner to corner

S² = 12² + 7²

S² = 144 + 49

S² = 193

S = √193 or -√193

Because we are dealing with lengths, we only want positive numbers. -√193 is not used. Thus S = √193

S = √193 = 13.8924439894

S = 18.92 (rounded to two places)

Thus, Reggie will cut 18.92 inches of paper.

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