SOLUTION: a 7cm by 10cm picture is mounted on a board with an equal border surrounding the picture. the area of the board is 208cm. what is width of border? helping son with quadratic equa

Algebra ->  Rectangles -> SOLUTION: a 7cm by 10cm picture is mounted on a board with an equal border surrounding the picture. the area of the board is 208cm. what is width of border? helping son with quadratic equa      Log On


   

Question 857604: a 7cm by 10cm picture is mounted on a board with an equal border surrounding the picture. the area of the board is 208cm. what is width of border? helping son with quadratic equations and stumped why answer is 3?
Answer by mananth(16946) About Me  (Show Source):
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a 7cm by 10cm picture is mounted on a board with an equal border surrounding the picture. the area of the board is 208cm. what is width of border? helping son with quadratic equations and stumped why answer is 3?

Area of picture = 7*10 = 70 cm^2

Let width be x on either side of length and width
length of board = 10+2x
Width of board = 7+2x
Area of board = 208 cm^2
Area = L*W
(10+2x)(7+2x) = 208
70+20x+14x+4x^2=208
4x^2+34x+70 = 208
4x^2+34x-138=0
/2
2x^2+17x-69=0
2x^2+23x-6x-69=0
2x(x+11.5)-6(x+11.5)=0
(2x-6)(x+11.5)=0
either 2x=6 OR x=-11.5
Ignore negative
2x=6
x= 3 cm
You can solve by squaring method or formula method.
Formula method
Find the roots of the equation by quadratic formula

a= 2 , b= 17 , c= -69

b^2-4ac= 289 + 552
b^2-4ac= 841
%09sqrt%28%09841%09%29=%0929%09
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( -17 + 29 )/ 4
x1= 3.00
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( -17 -29 ) / 4
x2= -11.50
Ignore negative value
x=3 cm