+1206 A painting with dimensions 10 inches by 14 inches is placed in a picture frame (of constant width), increasing its area to 221 square inches. How many inches is the width of the picture frame?
+36915 x = width of frame
original height 10 new height 10 + 2x
original width 14 new width 14 + 2x
and
(10+ 2x)(14+2x) = 221
4x^2+48x -81 = 0 Use quadratic Formula to find x = 1.5 inch width of frame
+128406 Let x be the width of the border......then one dimension of the picture and frame = ( 10 + 2x)
And the other dimension of the picture and frame = ( 14 + 2x)
So....the area =
(10 + 2x) ( 14 + 2x) = 221 simplify
140 + 28x + 20x + 4x^2 = 221
4x^2 + 48x + 140 = 221 subtract 221 from both sides
4x^2 + 48x - 81 = 0 factor
(2x - 3) (2x+ 27) = 0 set each factor to 0 and solve for x
(2x - 3) = 0 2x + 27 = 0
2x = 3 2x = -27
x = 3/2 = 1.5 inches x = -27/2 = - 13.5 reject
So.....the width is 1.5 inches
