Quadratic functions long question?
2014-10-10 8:03 am
A rectangular portrait measures 50cm by 70cm. It is just surrounded by a rectangular frame of uniform width. If the area of the frame is the same as the area of the portrait, what is the approximate width of the frame?
回答 (1)
2014-10-10 10:37 am
If w is the width of the frame, you have
.. 2(50*70) = (50+2w)(70+2w)
.. 7000 = 3500 + 240w + 4w^2
.. 0 = 4w^2 + 240w - 3500
.. 0 = w^2 + 60w - 875
.. w = (-60 ± √(60^2 - 4(1)(-875)))/2(1)
.. w = (-60 ± √7100)/2 = -30 ± √1775
.. w ≈ 12.13 … cm
_____
Check:
(50+2w)(70+2w) = 74.26*94.26 = 6999.75 ≈ 7000 … answer checks
.. 2(50*70) = (50+2w)(70+2w)
.. 7000 = 3500 + 240w + 4w^2
.. 0 = 4w^2 + 240w - 3500
.. 0 = w^2 + 60w - 875
.. w = (-60 ± √(60^2 - 4(1)(-875)))/2(1)
.. w = (-60 ± √7100)/2 = -30 ± √1775
.. w ≈ 12.13 … cm
_____
Check:
(50+2w)(70+2w) = 74.26*94.26 = 6999.75 ≈ 7000 … answer checks
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