Answer:
Length: 30.25 inches
Width: 23 inches
Step-by-step explanation:
Let
x ---> the length of the picture in inches
y ---> the width of the picture in inches
we know that
The perimeter of the picture is equal to
[tex]P=2(x+y)[/tex]
we have
[tex]P=106.5\ in[/tex]
so
[tex]106.5=2(x+y)[/tex]
simplify
[tex]53.25=x+y[/tex] ----> equation A
[tex]x=2y-15.75[/tex] ----> equation B
Solve the system by substitution
substitute equation B in equation A
[tex]53.25=(2y-15.75)+y[/tex]
solve for y
[tex]53.25+15.75=2y+y[/tex]
[tex]3y=69[/tex]
[tex]y=23\ in[/tex]
Find the value of x
[tex]x=2(23)-15.75=30.25\ in[/tex]
therefore
The dimensions of the picture are
Length: 30.25 inches
Width: 23 inches
