SOLUTION: A photograph is 16 inches wide and 9 inches long and is surrounded by a frame of uniform width x. If the area of the frame is 84 square inches, find the uniform width of the frame.

Question 923802: A photograph is 16 inches wide and 9 inches long and is surrounded by a frame of uniform width x. If the area of the frame is 84 square inches, find the uniform width of the frame.
a. What is the area of the photograph and frame?
b. Given the area of the frame which is 84 square inches, formulate the relationship among three areas and simplify.
I'm not sure about letter b but is the equation a(w)= (16+2x)(9+2x) or a(w)= 4x^2+25x+144 correct?
And I'm not sure if I should just add the two areas for letter 'a' or the area given for the frame is just the area of its borders/sides with the portion of the picture cut out.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Dimensions of picture, 16 and 9 inches.

Area of the picture, 16*9.
Area of picture AND frame, (16+2x)(9+2x).
Area of just the franem 84 sq.inchs.

, meaning the difference in area between the picture&frame combination and the picture will equal the area of the frame by itself.

That is a formulation among the known values and the unknown width of the frame; but was not any attempt at formulating a function. Still, you can solve for x, the uniform frame width.

Simplification is producing .
Applying the general solution of a quadratic equation and taking only the PLUS square root form, .
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