A straw is placed inside a rectangular box that is 5 inches by 10 inches by 4 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to
the top right back corner, how long is the straw? Leave your answer in simplest
radical form.

3x + 4y -25 =0 represents the amount of change sianna should recieve

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

answer4 to the second power is 16

and 4 to the third power is 64,