SOLUTION: A picture that measures 10 cm by 5 cm is to be surrounded by a mat before being framed. The width of the mat is to be the same on all sides of the picture. The area of the mat is t

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Question 378676: A picture that measures 10 cm by 5 cm is to be surrounded by a mat before being framed. The width of the mat is to be the same on all sides of the picture. The area of the mat is to be twice the area of the picture. What is the width of the mat?
Answer by mananth(16946) About Me  (Show Source):
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A picture that measures 10 cm by 5 cm is to be surrounded by a mat before being framed. The width of the mat is to be the same on all sides of the picture. The area of the mat is to be twice the area of the picture.
...
Area of picture = 10*5 = 50 cm^2
Area of mat = 2*50 = 100 cm^2
...
let width of mat be x
width of frame including mat = 2x+5cm ( x on each side)
length = 2x+10
..
Total Area = (2x+5)(2x+10)
area of picture = 50 cm^2
area of mat = 100 cm^2
..
(2x+5)(2x+10)-50 =100
4x^2+30x+50-50=100
4x^2+30x=100
/2
2x^2+15x=50
-75
2x^2+15x-50=0
solve using quadratic formula
x1= (-15+sqrt(225+200))/4
x1=(-15+(sqrt(625))/4
x1= 2.5 cm the width of the mat
x2 is negative so ignore
...
m.ananth@hotmail.ca