A rectangular picture is 3cm longer than its width, (x+3). A frame 1 cm wide is placed around the picture. The area of the frame alone is 42 cm^2. Find the length of the picture _______cm.

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**(try my best to draw a pic frame***

diagram is mess up =(

To find the length of the picture, we need to find the width and the length of the entire rectangular shape, including the frame.

Let's start by finding the width of the picture.

We are given that the length of the picture is 3cm longer than its width, so we can say x + 3 represents the length of the picture.

We are also given that there is a 1cm frame around the picture. This means that the total width of the rectangular shape, including the frame, is (x + 3) + 2 * 1 cm, which simplifies to (x + 5) cm.

Now, let's find the area of just the frame. We are given that the area of the frame alone is 42 cm^2.

The area of a rectangle is equal to its length multiplied by its width. Since the frame is a rectangle, we can write the equation:

Area of Frame = Length of Frame * Width of Frame

Substituting the values we have:

42 cm^2 = 1 cm * (x + 5) cm

Now, we can solve this equation to find the value of x:

42 cm^2 = x + 5 cm

Subtracting 5 cm from both sides:

42 cm^2 - 5 cm = x

37 cm = x

Therefore, the width of the picture is 37 cm.

To find the length of the picture, we can substitute the value of x into the equation for the length:

Length of Picture = x + 3 cm

Length of Picture = 37 cm + 3 cm

Length of Picture = 40 cm

So, the length of the picture is 40 cm.