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Sagot :
The 4•x by 5•x inner dimensions of the 53 inches outer perimeter picture frame, the 1 inch wide frame and the 4 × 5 inch picture to be enlarged, gives;
a. The outer perimeter equation is presented as follows;
18•x + 8 = 53 inches
b. The scale factor required for the enlargement of the picture is 2.5
Which method can be used to write the equation and find the scale factor?
The dimensions of the photo = 4 × 5 inch
Width of the frame = 1 inch
Outer perimeter of the frame = 53 inches
The width of the inside of the picture frame = 4•x
The height of the inside of the picture frame = 5•x
a. The equation for the outer perimeter of the picture frame is therefore;
2 × (4•x + 1 + 1) + 2 × (5•x + 1 + 1) = 53
Which gives;
2 × (4•x + 2) + 2 × (5•x + 2) = 53
8•x + 4 + 10•x + 4 = 53
A simplified equation for the outer perimeter of the picture frame is therefore;
- 18•x + 8 = 53
b. Solving the above equation, we have;
18•x + 8 = 53
18•x = 53 - 8 = 45
18•x = 45
Therefore;
x = 45 ÷ 18 = 2.5
x = 2.5
The width and height of the picture frame are therefore;
Width = 4•x = 4 × 2.5 = 10
Height = 5•x = 5 × 2.5 = 12.5
Which gives;
Width = 10 inches
Height = 12.5 inches
The enlargement factor, sf, is given by the ratio of a side of the picture frame to a side of the picture as follows;
sf = 12.5/5 = 2.5
- The factor by which to enlarge the picture frame is 2.5
Learn more about linear scale factors here:
https://brainly.com/question/19381630
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