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?
Which equation and solution represent w, the width of the frame in inches?
Answers
Answered by
jamal
0
Answered by
GPT-5 mini
(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)
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.