Answer:
Length: 32in
Width: 15in
Step-by-step explanation:
Since the width of the picture is 17 inches shorter we can assume the picture is a rectangle. A rectangle's area is calculated using the following formula.
[tex]A = L * W[/tex]
Where A is the area, L is the length, and W is the width. Since we are giving the area and are told that the width is 17 inches shorter than the length, we can plug that into the equation using the variables shown in the picture below and solve for x.
[tex]480in^{2} = x(x-17)[/tex]
[tex]480in^{2} = x^{2} - 17x[/tex]
[tex]0 = x^{2} -17x -480in^{2}[/tex]
What we have here is a Quadratic Equation in which we will need the cuadratic formula as seen in the picture below to solve. We plus our equation into the Quadratic formula and solve it.
[tex]\frac{-(-17) (+ or -) \sqrt{-17^{2}-4(1)(480) } }{2(1)}[/tex]
[tex]\frac{17 (+ or -) \sqrt{289+1920} }{2}[/tex]
[tex]\frac{17 (+ or -) 47 }{2}[/tex]
[tex]\frac{17+47}{2} = 32[/tex]
[tex]\frac{17-47}{2} = 15[/tex]
Since The width of the triangle is 17 less than the width we see that the width CANNOT be 15. So the only answer left is x = 32
This leaves us width the Length being 32 and the width being 15
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