Question

John has a rectangular picture which is 43 inches long and 27 inches wide. He wants to build a wooden gram for the picture but she only has 800 square inches of wood available. How wide will the border be?

Answer 1

5 inches

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,

`A=(43+2x)(27+2x)-----(1)`

Now, the area of the picture,

`A_1=43* 27=1161\text{ square inches}----(2)`

We have, the area of the border,

`A_2=800\text{ square inches}----(3)`

Thus,

`A=A_1+A_2`

Equation (1) (2) and (3),

`(43+2x)(27+2x) = 1161+800`

`1161 + 86x+54x+4x^2=1161+800`

`4x^2+140x-800=0`

`x^2+35x-200=0`

`x^2+40x-5x-200=0`

`x(x+40)-5(x+40)=0`

`(x-5)(x+40)=0`

`\implies x=5\text{ or }x=-40`

∵ Width can not be negative,

Hence, the width of the border is 5 inches.

Answer 2

The border will be 18.6 inches wide

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.

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