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gizmo_the_mogwai [7]
3 years ago
13

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 s

he only has 800 square inches of wood available. How wide will the border be?
Mathematics
2 answers:
Lelechka [254]3 years ago
7 0

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,

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

Now, the area of the picture,

A_1=43\times 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.

Dvinal [7]3 years ago
5 0

Answer:

The border will be 18.6 inches wide

Step-by-step explanation:

<em>Let the width be w</em>

<em>The length = 43 inches</em>

<em>Total wood = 800 square inches</em>

Formula for area of rectangle = length x width

<em>800 = 43 x w</em>

<em>w = 800/43</em>

w = 18.6 inches

Therefore, the border will be 18.6 inches wide.

!!

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