SOLUTION: A picture that measures 10cm by 8cm is to be surrounded by a mat before framing. The width of the mat is to be the same on all sides of the picture. The area of the mat is equal to

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: A picture that measures 10cm by 8cm is to be surrounded by a mat before framing. The width of the mat is to be the same on all sides of the picture. The area of the mat is equal to      Log On


   

Question 288724: A picture that measures 10cm by 8cm is to be surrounded by a mat before framing. The width of the mat is to be the same on all sides of the picture. The area of the mat is equal to the area of the picture. What is the width of the mat, to the nearest tenth of a centimetre?
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
10*8=80 cm^2 is the area of the picture.
(10+2x)(8+2x)-80=80
80+16x+20x+4x^2-160=0
4x^2+36x-80=0
4(x^2+9x-20)=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=(-9+-sqrt[9^2-4*1*-20])/2*1
x=(-9+-sqrt[81+80])/2
x=(-9+-sqrt161)/2
x=(-9+-12.69)/2
x=(-9+-12.69)/2
x=(-9+12.69)/2
x=3.69/2
x=1.8 cm. is the width of the mat.
Proof:
(10+2*1.8)(8+2*1.8)-80=80
(10+3.6)(8+3.6)=160
13.8*11.6=160
160~160