9. what is the longest flagpole (in whole feet) that could be
shipped in a box that measures 2 ft by 2 ft by 12 ft?
12 ft

Step-by-step explanation:

If the pole lies flat on one side of the box, with one end in each of the two opposite vertices of the box, and d represents the length of the pole, then:

d² = 12² + 2², or d² = 144 + 4 = 148 ft².  d (the longest pole length) would then be 12.17 ft.

If the pole has one vertex in one of the four lower corners of the box, and if it reaches diagonally to the opposite vertex 2 feet up, then:

d² = 2² + 2² + 12², or 4 + 4 + 144 (all in ft²).  Then d = 12.33 ft.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.