8m Picture Frame
8m Picture Frame
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Problems involving quadratic equations?
1) A carpet is placed in a room 6m by 4m, leaving a border of uniform width all round it. Find the width of the border if the area of the carpet is 8m^2.
2) A picture on a wall measures 24 cm,by 20cm. It is surrounded by a frame of uniform width whose area is 416cm^2. What us the width of the frame?
Please HELP!
1.)
let x = width of border
l = 6m - 2x
w = 4m - 2x
and
A = l * w
so
A = (6m - 2x)(4m - 2x)
8 = 4x^2 - 20x + 24
4x^2 - 20x + 16 = 0
x = 4, or x = 1
4 m does not make sense since it would create lengths and widths less than 0,
so x = 1 m is your solution.
2.)
let x = frame border width
l = frame length
w = overall frame width
A = area of frame
l = 24 + 2x
w = 20 + 2x
Area of frame = overall area minus picture area
A = l*w - 24*20
416 = (24+2x)(20 + 2x) - 480
416 = 480 +88x + 4x^2 - 480
4x^2 + 88x -416 = 0
x = 4
x = -26
(x = -26 makes no sense)
so
x = 4 cm is your answer
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