SOLUTION: A square painting is surrounded by a 2.5 cm frame.If the total area of the painting plus frame is 3600 sq cm, find the dimensions of painting

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Question 949644: A square painting is surrounded by a 2.5 cm frame.If the total area of the painting plus frame is 3600 sq cm, find the dimensions of painting
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Assign variables to everything, and use a drawing to help.
x, the side length of the square painting
w, the uniform width around the painting
A, area of frame plus the painting
Given values:
x, unknown
w=2.5 cm
A=3600 square cm

Total Area, %28x%2B2w%29%5E2=A

x%5E2%2B4wx%2B4w%5E2-A=0
Solving process can continue completely in symbols but easier here to
plug in the given values now.
x%5E2%2B4%282.5%29x%2B4%282.5%29%5E2-3600=0
highlight_green%28x%5E2%2B10x-3575=0%29

Discriminant is 100%2B4%283575%29=14400=%28120%29%5E2

x=%28-10%2B-+sqrt%28120%5E2%29%29%2F2

x=%28-10%2B-+120%29%2F2=highlight_green%28-5%2B-+60%29

The MINUS 60 form makes no sense, so use the PLUS form.
highlight%28x=55%29