A photograph print measuring 24cm by 15cm is enclosed in a frame A uniform space of width xcm is left in between the edges of the photograph and the frame.if the area of the space is 270cm2 ,find the value of x
AAAaannndd the bot gets it wrong yet again!
4x^2 + 78x - 270 = 2(x-3)(2x+45)
so x=3
The overall dimensions of the framed photograph are:
Length = 24 + 2x
Width = 15 + 2x
The area of the space between the photograph and the frame is:
Area = overall area - photograph area
270 = (24 + 2x)(15 + 2x) - (24)(15)
270 = 360 + 78x + 4x^2 - 360
0 = 4x^2 + 78x - 270
Using the quadratic formula:
x = (-78 ± sqrt(78^2 - 4(4)(-270))) / (2(4))
x = (-78 ± sqrt(6768)) / 8
x = (-78 ± 82.3) / 8
x can equal either -20.075 or 1.575. Since a width of negative length does not make sense, we discard the negative answer.
Therefore, the value of x is 1.575 cm.