17. The expression x2 - 12x + 36 represents the area of a rectangular chalkboard. What is the factored
form of the expression? If each factor represents the
height and width of the chalkboard, what is the most
specic description of its shape?
A.(x-6), square
c B. (X - 5)(x + 6); rectangle
C. (x + 5)2: square
D. (x - 12): square

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

it’s the first one your welcome