13.148. A photograph measuring $12 \times 18$ cm is inserted into a frame of constant width. Determine the width of the frame if its area is equal to the area of the photograph itself.
## Solution.

Let $x$ cm be the width of the frame (Fig. 13.9). Then its area is $2 \cdot 12 x + 2(18 + 2 x) x$ cm. According to the condition, $2 \cdot 12 x + 2(18 + 2 x) x = 12 \cdot 18$, from

![](https://cdn.mathpix.com/cropped/2024_05_22_fa9db84b44b98ec0a5c7g-874.jpg?height=368&width=516&top_left_y=688&top_left_x=702)

Fig. 13.9 where $x=3$ cm.

Answer: 3 cm.