the length of a rectangular photograph is 8in. more than the width. if the area is 560 in^2 what are the dimensions of the photograph?
the width is______ in. and the length is _______ in.
help? thanks!
To find the dimensions of the photograph, we can solve this problem using algebra.
Let's assume that the width of the photograph is x inches. According to the given information, the length of the photograph is 8 inches more than the width. So, the length would be x + 8 inches.
The area of a rectangle is given by the formula: Area = Length × Width.
Given that the area of the photograph is 560 square inches, we can set up an equation:
(x + 8) × x = 560
Expanding this equation, we get:
x^2 + 8x = 560
Rearranging the equation to get it in quadratic form:
x^2 + 8x - 560 = 0
To solve this quadratic equation, we can factor it or apply the quadratic formula. In this case, let's factor the equation:
(x + 28)(x - 20) = 0
Setting each factor equal to zero, we get:
x + 28 = 0 or x - 20 = 0
Solving these equations, we find two possible values for the width:
x = -28 or x = 20
Since width cannot be negative, we discard x = -28. Thus, the width of the photograph is 20 inches.
Now, substitute this value into our earlier expression for the length:
Length = x + 8 = 20 + 8 = 28 inches.
Therefore, the width of the photograph is 20 inches, and the length is 28 inches.