Question

The figure below shows two similar pictures that Jeremy wants to frame.



Jeremy has 5 strips of unfinished molding that he wants to use to frame the two pictures. Each strip is 36 inches long.

Assuming there is no wastage or overlap of molding, what is the minimum length of molding, in inches, Jeremy still requires to frame both the pictures? Show your work and explain your reasoning in complete sentences.

Answer 1

Okay so, we'll use a little geometry,
similar means that they are grown in a proportion so:
let's name them ABCD and A'B'C'D'.
we say, by definition of similarity that:
\[\frac{ A' }{ A }=\frac{ B' }{ B }=\frac{ C' }{ C }=\frac{ D' }{ D }\]
that said and done:
we take the lenght of one of the figures and divide it by it's similar.
58.5/13 = 4.5
All you do is take the lenghts, multiply them by 4.5 and calculate the perimeter.
That would be the molding you need to frame them.

Answer 2

perimeter of small pic = 2(16+13) = 2(29) = 58

scale factor = 58.5/13 = 4.5
that means, lengths in left side pic is 4.5 times larger than right side.
so perimeter of big pic = 4.5 x 58 = 261

total length = 58 + 261 = 319


length of molding available = 5x36 = 180

319 - 180 = 139

so, he requires 139in more of molding