Algebra problem - simple but needs working

This problem can be solved intuitively.

But how do you show it using just algebra?

Can anyone answer this with all working ONLY algebraically?

A square photo has a border 5 cm wide.
The photo area is 4/9 of the total area.
Find the area of the photo.

if the width of the photo is x
the width of the frame is x+10

area of the photo = x^2
total area = (x+10)^2

but

area of the photo=4/9*total area
x^2 = 4/9*(x+10)^2

taking the square root of both sides
x = 2/3*(x+10)
3x=2x+20
x=20

area of the photo = x^2=400 cm2

have fun!!!!!!!!!

Side of the square—x:
4/9(x + 2[5])² = x²
4(x + 10)² = 9x²
4(x² + 10x + 10x + 100) = 9x²
4(x² + 20x + 100) = 9x²
4x² + 80x + 400 = 9x²
5x² - 80x = 400
x² - 8x = 80 + (- 8)²
x² - 8x = 80 + 64
(x - 8)² = 144
x - 8 = 12
x = 20

Area of the photo:
= 20²
= 400

Answer: 400 sq cm

Check:
= 400/(20 + 10)²
= 400/30²
= 400/900 OR (400/100)/(900/100)
= 4/9

Photo + Frame = 5^2

Total Area = 25 cm^2

Photo = (4/9) * Total Area

Photo = (4/9)*(25)

Photo = 100/9

Photo Area = 11 1/9 cm^2............ANSWER

5*5 = 25 cm^2 it total area; 4/9*5*5= 11.111 is the area of the photo

A = (5^2) * (4/9)