justify conclusions

Question

rodrigo is buying a 5 1/2-foot-long fishing rod for his father for his birthday. he wants to put it in a box so that his dad will not be able to guess what is in the box. the box he wants to use is 4 feet long and 4 feet wide. will the pole fit in the box? justify your reasoning.

Answer 1

ANSWER: Yes, the rod will fit in the box

 

The longest length in the box will be the diagonal. The diagonal is the hypotenuse of a right triangle with one side being the length and the other side being the width.

 

Use the Pythagorean theorem to calculate the length of this hypotenuse. Pythagorean theorem is a^2+b^2=c^2 where c is the length of the hypotenuse and a and b are the lengths of the sides (4 in this problem)

 

a^2+b^2=c^2

4^2+4^2=c^2

16+16=c^2

32=c^2

sqrt(32)=c; In this step, I simply took the square root of each side

5.66=c

 

Therefore, the length of the hypotenuse, which is the diagonal of the box, is 5.66 feet. Since the rod is only 5.5 feet long, then it will fit in the box.