To find the length of the photograph, we need to first set up the equation based on the information provided.
- The width of the photograph is \( x \) inches.
- The length of the photograph, being 3 inches longer than the width, is \( x + 3 \) inches.
- The area of the photograph is given by the expression \( x(x + 3) \) square inches.
According to the problem, the area is also equal to 70 square inches. Therefore, we can set up the equation:
\[ x(x + 3) = 70 \]
Expanding this equation, we get:
\[ x^2 + 3x = 70 \]
Now, we move 70 to the left side to set the equation to zero:
\[ x^2 + 3x - 70 = 0 \]
Next, we can factor this quadratic equation. We are looking for two numbers that multiply to \(-70\) and add to \(3\). The numbers \(10\) and \(-7\) fit this description:
\[ (x + 10)(x - 7) = 0 \]
Setting each factor to zero gives us:
\[ x + 10 = 0 \quad \text{or} \quad x - 7 = 0 \] \[ x = -10 \quad \text{or} \quad x = 7 \]
Since \( x \) represents a length, it must be positive, so we take:
\[ x = 7 \]
Now we can find the length of the photograph:
\[ \text{Length} = x + 3 = 7 + 3 = 10 \text{ inches} \]
Thus, the length of the photograph is:
\[ \boxed{10} \text{ inches} \]
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