Final answer:
The value of x that solves the equation for the area of the rectangular picture is 10 cm. This makes the dimensions of the picture 22 cm by 20 cm.
Step-by-step explanation:
To find the value of x for the rectangular picture with area 360 cm² and dimensions (x+10) cm by (x+12) cm, we need to solve the equation given by the area of a rectangle, which is the product of its length and width. That is:
(x+10)(x+12) = 360
Expanding the equation:
x² + 12x + 10x + 120 = 360
x² + 22x + 120 - 360 = 0
x² + 22x - 240 = 0
This is a quadratic equation. By factoring or using the quadratic formula, we find that:
x = 10 or x = -24
Since the dimensions of a picture cannot be negative, we choose x = 10. Therefore, the dimensions of the picture are:
Length: (10+12) cm = 22 cm
Width: (10+10) cm = 20 cm