Question

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.

Answer 1

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.