Question

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

Answer 1

Width of Pathway; 2 meters

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;

Solution; Width ⇒ 2 meters

Answer 2

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