Question

A square picture has a 1-inch frame around it. If the area of the frame alone is 36 in.2, what is the area of the picture?

Answer 1

Answer:

Area of square picture = 64 inch²

Step-by-step explanation:

Let the side of picture be a,

A square picture has a 1-inch frame around it.

Area of frame = Area of square of a + 2 side - Area of square of a  side

36 = (a+2)² - a²

a² + 4a + 4 -a² = 36

4a+4 = 36

a = 8 inches.

Side length of square picture = 8 inches

Area of square picture = 8 x 8 = 64 inch²

Answer 2

Answer:

The area of the picture is $64\ in^{2}$

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

$36=(x+2)^{2}-x^{2} \\36=x^{2}+4x+4-x^{2} \\ 36=4x+4\\4x=36-4\\x=32/4\\x=8\ in$

The area of the picture is

$A=x^{2}$

$A=64\ in^{2}$