SOLUTION: A rectangular painting by a local artist is 3ft.taller than it is wide. if the wooden frame is 12 inch wide, the combined area of the picture and frame is 208 square ft. Find the d

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A rectangular painting by a local artist is 3ft.taller than it is wide. if the wooden frame is 12 inch wide, the combined area of the picture and frame is 208 square ft. Find the d      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 388984: A rectangular painting by a local artist is 3ft.taller than it is wide. if the wooden frame is 12 inch wide, the combined area of the picture and frame is 208 square ft. Find the dimensions of the painting by itself.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let h = total height
Let w = total width
given:
h%2Aw+=+208
h+=+w+%2B+3
-----------
%28w%2B3%29%2Aw+=+208
w%5E2+%2B+3w+-+208+=+0
w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+3
c+=+-208
w+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-208%29+%29%29%2F%282%2A1%29+
w+=+%28-3+%2B-+sqrt%28+9+%2B+832+%29%29%2F2+
w+=+%28-3+%2B-+sqrt%28+841+%29%29%2F2+
w+=+%28-3+%2B+29%29%2F2+
w+=26%2F2
w+=+13 (the other root is negative)
and
h+=+w+%2B+3
h+=+16
The frame subtracts 2 ft from both the height and the width, so
w+-+2+=+11
h+-+2+=+14
The painting alone is 11 ft by 14 ft