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chubhunter [2.5K]
3 years ago
12

A garden measuring 12 meters by 6 meters is going to have a walkway constructed all around the perimeter, increasing the total a

rea to 160 square meters. What will be the width of the pathway? (The pathway will be the same width around the entire garden).
Pls Show Work
Mathematics
2 answers:
Lostsunrise [7]3 years ago
8 0

Answer:

x=2 meters

Step-by-step explanation:

length = 12+2x

width = 6+2x

Area = (12+2x) (6+2x) = 160

Foil

 72 + 12x+24x+4x^2 = 160

Combine like terms

4x^2 + 36x +72 = 160

Subtract 160 from each side

4x^2 +36x -88 =0

Divide by 4

x^2 +9x -22=0

Factor

What 2 numbers multiply to -22 and add to 9

11 * -2 = -22

11+ -2 = 9

(x +11) (x-2) =0

Using the zero product property

x=-11  x=2

Since we cant have negative length

x=2

makkiz [27]3 years ago
3 0

Answer:

<em>Width of Pathway; 2 meters</em>

Step-by-step explanation:

To determine the width of the pathway we can tell that the length of the ends ( in meters ) is distributed among the two other ends of the garden so that the width ⇒

Increase length on one side * 2, if increased length / width ⇒ x, 2x

From this we can formulate an equation based on the lengths of the garden, as the increased lengths represents the side lengths of the total area ( walkway + garden );

( 12 + 2x )( 6 + 2x ) = 160 ⇒ Expand,

72 + 36x + 4x^2 = 160 ⇒ Subtract 160 on either side,

4x^2 + 36x - 88 = 0 ⇒ Factor,

4 * ( x - 2 ) * ( x + 11 ) = 0 ⇒ Use Zero Factor Principle,

x = 2, and x = - 11;

Now the width can only be a positive value, thus;

<em>Solution; Width ⇒ 2 meters</em>

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