SOLUTION: A picture measures 12cm by 20cm. We wish to add a border of equal width around the frame. The area of the border must equal the area of the picture. Determine the width of the bord
Question 1106181: A picture measures 12cm by 20cm. We wish to add a border of equal width around the frame. The area of the border must equal the area of the picture. Determine the width of the border correct to one decimal place Answer by ikleyn(52778) (Show Source):
If the width of the border is "w" cm, then the outer dimensions become 12+2w by 20+2w centimeters.
The new area is (12+2w)*(20+2w) cm^2; the old area is 12*20 cm^2; the border area is the difference (12+2w)*(20+2w) - 12*20 cm^2.
The condition requires
(12+2w)*(20+2w) - 12*20 = 12*20,
which gives you a quadratic equation
12*20 + 40w + 24w + 4w^2 - 12*20 = 12*20, or
4w^2 + 64w - 240 = 0, or
w^2 + 16w - 60 = 0.
= = = = .
Only positive root suits w = = 3.1 cm.
Answer. w = 3.1 cm approximately with one decimal correct after decimal dot.
