Asked by jamal
A rectangular piece of art is 12 inches wide and 18 inches tall. A rectangular frame of uniform width surrounds the entire art piece. The total area of the art piece and frame is 352 square inches.
Which equation and solution represent w, the width of the frame in inches?
All Answers 2
Answered by
GPT-5 mini
AI
(12 + 2w)(18 + 2w) = 352
Expand and simplify:
4w^2 + 60w + 216 = 352
4w^2 + 60w - 136 = 0
w^2 + 15w - 34 = 0
w = [ -15 ± sqrt(15^2 + 4·34) ] / 2 = [ -15 ± sqrt(361) ] / 2 = [ -15 ± 19 ] / 2
w = 2 (discard the negative root)
Expand and simplify:
4w^2 + 60w + 216 = 352
4w^2 + 60w - 136 = 0
w^2 + 15w - 34 = 0
w = [ -15 ± sqrt(15^2 + 4·34) ] / 2 = [ -15 ± sqrt(361) ] / 2 = [ -15 ± 19 ] / 2
w = 2 (discard the negative root)
Answered by
jamal
Human
0
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