Answer:
2.5
Step-by-step explanation:
A rectangular picture is 12 by 16 inches.
the area of the frame is 165 sq inches
the frame borders the pictures round the 4 corners
for the length, Let x be the frame distance to the picture which is 12+x+x= 12+2x
and for the breadth, Let x be the frame distance to the picture which is 16+x+x = 16+2x
(12+2x) x (16+2x) = length x breadth of frame
12(16+2x)+2x(16+2x)
192+24x+32x+4x²
192+56x+4x² is the area of frame
165 is area of frame - area of rectangular picture
165 = 192+56x+4x² - (12 x16)
165 = 192+56x+4x² - 192
165 = 56x+4x²
subtract 165 from both sides to form a quadratic equation
4x²+56x-165= 0
using almighty formula
x=-b±√b²-4ac/2a
a= 4
b=56
c=-165
x=-b±√b²-4ac/2a = -56±√56²-4(4)(-165)/2(4)
= -56±√3136+2640/8= -56±√5776/8 = -56±76/8
splitting the sign±
-56+76/8 ,-56-76/8
20/8, -132/8
5/2, -16.5
2.5, -16.5
we need to neglect the neagtive answer because the width cant be negative
the width is 2.5
