Answer :
Answer:
Length = 45.37 in
Width = 30.56 in
Step-by-step explanation:
Let the width of the picture be 'w' inches.
Given:
Perimeter of the picture is, [tex]P=106.5\ in[/tex]
Length is 15.75 inches shorter than twice the width. So, length is:
[tex]l=2w-15.75[/tex]
Now, we know that the perimeter of a rectangular shape is given as the sum of all of its side. So, the picture is also of rectangular shape and hence the perimeter is given as:
[tex]P=2l+2w[/tex]
Plug in the values of 'l' and 'P' and solve for 'w'. This gives,
[tex]106.5=2w-15.75+2w\\106.5=4w-15.75\\106.5+15.75=4w\\4w=122.25\\w=\frac{122.25}{4}=30.56\ in[/tex]
Therefore, the width of the rectangular picture is 30.56 inches.
Length of the picture is, [tex]l=2(30.56)-15.75=61.12-15.75=45.37\ in[/tex]
So, length of the picture is 45.37 inches and width is 30.56 inches.