SOLUTION: A rectangular picture measuring 4 in. by 10 in. is surrounded by a frame with uniform width x. Write a quadratic function in standard form to show the combined area of the picture

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A rectangular picture measuring 4 in. by 10 in. is surrounded by a frame with uniform width x. Write a quadratic function in standard form to show the combined area of the picture      Log On


   

Question 637359: A rectangular picture measuring 4 in. by 10 in. is surrounded by a frame with uniform width x. Write a quadratic function in standard form to show the combined area of the picture and frame.
Answer by Stitch(470) About Me  (Show Source):
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Since the frame is uniform around the picture, you have to add the distance of the frame to dimensions of the picture.
The 4in length will now become: X + 4 + X or 2x + 4.
The 10in width will now be: X + 10 + X or 2X + 10
Area is found by multiplying the length by the width.
A = L * W
In our case L = 2X + 4
And W = 2X + 10
A = (2X + 4) * (2X + 10)
Now simplify the equation by multiplying through.
A = 4X^2 + 20X + 8X + 40
Combine like terms
A = 4X^2 + 28X + 40