An artist is creating a large painting from a photograph by dividing the photograph into squares and dilating each square by a factor of 4. if the photograph is 4 in. by 6in., what is the perimeter of the painting?

80 in.
384 in.
28 in.

  80 in.

Step-by-step explanation:

The dimensions of the dilated picture are ...

  4·4 in = 16 in . . . by . . . 4·6 in = 24 in

Then the perimeter of the painting is the sum of the lengths of its sides ...

  16 in + 24 in + 16 in + 24 in = 80 in

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

answer: you need to organize this better it does not make sense.

step-by-step explanation: ?