Answer:
The area of the picture is [tex]64\ in^{2}[/tex]
Step-by-step explanation:
Let
x-----> the length side of the square picture
we know that
The area of the picture plus the frame minus the area of the picture is equal to the area of the frame alone
[tex]36=(x+2)^{2}-x^{2} \\36=x^{2}+4x+4-x^{2} \\ 36=4x+4\\4x=36-4\\x=32/4\\x=8\ in[/tex]
The area of the picture is
[tex]A=x^{2}[/tex]
[tex]A=64\ in^{2}[/tex]
This question is based on the area of square. Therefore, the area of the picture is 64 [tex]in^{2}[/tex] .
Given:
A square picture has a 1-inch frame around it. If the area of the frame alone is 36 [tex]inch^{2}[/tex].
We need to determined the area of the square picture.
Let x be the length side of the square picture.
As we know that,
The area of the picture and the frame minus the area of the picture is equal to the area of the frame alone.
[tex]36 = (x+2)^{2} -x^{2} \\36 = x^{2} +4+4x-x^{2} \\36-4=4x\\\dfrac{32}{4}= x\\x=8[/tex]
And we know that area of square picture is =[tex]x^{2}[/tex]
= [tex]8^{2} = 64\; inch^{2}[/tex].
Therefore, the area of the picture is 64 [tex]in^{2}[/tex] .
For more details, please prefer this link:
https://brainly.com/question/11505374
