Answer:
The border will be 18.6 inches wide
Step-by-step explanation:
Let the width be w
The length = 43 inches
Total wood = 800 square inches
Formula for area of rectangle = length x width
800 = 43 x w
w = 800/43
w = 18.6 inches
Therefore, the border will be 18.6 inches wide.
!!
Answer:
5 inches
Step-by-step explanation:
Let x be the width ( in inches ) of the border,
Given,
The length of the picture = 43 inches,
And, width of the picture = 27 inches,
So, the length of whole frame ( picture with border ) = 43 + 2x,
Its width = 27 + 2x
Thus, the area of the whole frame,
[tex]A=(43+2x)(27+2x)-----(1)[/tex]
Now, the area of the picture,
[tex]A_1=43\times 27=1161\text{ square inches}----(2)[/tex]
We have, the area of the border,
[tex]A_2=800\text{ square inches}----(3)[/tex]
Thus,
[tex]A=A_1+A_2[/tex]
Equation (1) (2) and (3),
[tex](43+2x)(27+2x) = 1161+800[/tex]
[tex]1161 + 86x+54x+4x^2=1161+800[/tex]
[tex]4x^2+140x-800=0[/tex]
[tex]x^2+35x-200=0[/tex]
[tex]x^2+40x-5x-200=0[/tex]
[tex]x(x+40)-5(x+40)=0[/tex]
[tex](x-5)(x+40)=0[/tex]
[tex]\implies x=5\text{ or }x=-40[/tex]
∵ Width can not be negative,
Hence, the width of the border is 5 inches.
