A photograph has a length that is 3 inches longer than its width, x. So its area is given by the expression x(x+3) square inches. If the area of the photograph is 70 square inches, what is the length of the photograph?
The length of the photograph is _____ inches.
what is 7x10?
To find the length of the photograph, we need to solve the equation x(x+3) = 70, since the area of the photograph is given by the expression x(x+3).
First, let's simplify the equation by multiplying out the expression x(x+3):
x(x+3) = 70
x^2 + 3x = 70
Now, let's rearrange the equation to set it equal to zero:
x^2 + 3x - 70 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's factor the equation:
(x + 10)(x - 7) = 0
Setting each factor equal to zero gives us two possible values for x:
x + 10 = 0 or x - 7 = 0
Solving each equation gives us:
x = -10 or x = 7
Since the width cannot be negative, we discard the solution x = -10.
Therefore, the width of the photograph is x = 7 inches. Since the length of the photograph is 3 inches longer than its width, the length is:
7 + 3 = 10 inches
So, the length of the photograph is 10 inches.