Respuesta :
Answer:
16x-64 square inches
Step-by-step explanation:
Given that a square painting is surrounded by a frame. The outside edges of the frame are x inches in length and there is a 4-inch border between the painting and the frame.
Thus the square frame consists of an outer square with side x inches and inner square with side x-4(2)
The area of the border
=
area of outer square-area of inner square
=x^2-(x-8)^2
= (2x-8)(8)
=16x-64
Area of square is the square of its sides length.The total area of the border is [tex]16x-64[/tex] squared inch.
Total area of the border between the frame and square painting has to be find out.
What is area of square?
Area of square is the square of its sides length. It can be given as,
[tex]A=a^2[/tex]
Here, [tex]a[/tex] is the length of the side of the square.
Given information-
A square painting is surrounded by a frame.
The outside edges of the frame are x inches in length.
There is a 4-inch border between the painting and frame.
As the length of the edges of the frame is [tex]x[/tex] inches long and border is 4 inch long between the painting and frame both sides. Thus the edge of the frame is,
[tex]=(x-(4+4))\\=(x-8)[/tex]
The total area of the border is the difference of the area of the frame and the area of the painting. Thus total area of the border is,
[tex]A_b=x^2+(x-8)^2\\A_b=x^2-(x^2+64-16x)\\A_b=x^2-x^2-64+16x\\A_b=16x-64[/tex]
Hence the total area of the border is [tex]16x-64[/tex] squared inch.
Learn more about the area of the square here;
https://brainly.com/question/1658516
