We are given that a box is 4 feet long and 4 feet wide. We want to determine whether a 5 12-foot-long fishing rod will fit in the box. Let's draw a square with a side length of 4 feet.
Let's calculate the length of the diagonal of this square! Notice that the diagonal is also the hypotenuse of a right triangle. This means that we can use the Pythagorean Theorem to find the missing length.
a^2+ b^2= c^2In the formula, a and b are the lengths of the legs and c is the length of the hypotenuse of a right triangle. We are given a triangle with a= 4 and b= 4.
Let's substitute these values into the formula.
a^2+ b^2= c^2
⇕
4^2+ 4^2= c^2
Now we can solve the equation that we got to find the value of c.
Since a negative side length does not make sense, we only need to consider positive solutions. Therefore, we got that the length of the diagonal of the square is about 5.7 feet. Now let's compare this length with the length of the fishing rod.
5 12 = 5.5 < 5.7
We found that the fishing rod is shorter than the diagonal of the bottom of the box. This means that the fishing rod will fit in the box!
