There is a garden in which the area is 32ft squared. It is surrounded by a 26ft fence. I need to figure out the length and width of the gardens fence using factoring

Answer 1

The easiest way to solve this problem is to create an equation system. We know the following:

Area: L × W = 32

Perimeter: 2L + 2W = 26

To solve a system of equations, rearrange one of the equations and substitute that value for the corresponding variable in the other equation:

2(L + W) = 26

L + W = 13

L = 13 – W

Substituting (13 – W) for L in the other equation:

L × W = 32

(13 – W) × W = 32

13W – W² = 32

–W² + 13W – 32 = 0

W² – 13W + 32 = 0

However, no rational factors can be used to solve this equation by factoring.

Answer 2

A=32 = Lw

P=26 = 2(L+w)

13=L+w

L=13-w

32 =(13-w)w = 13w-w^2

w^2 -13w +32=0

no integer or rational factors

(w-6.5 +.5sqr41 )(w-6.5-.5sqr41 ) = 0

or about

(w-9.7)(w-3.3) = 0

width = about 3.3 feet

Length = about 9.7 feet

use the quadratic formula

w=13/2 +/-.5sqr(169-128)

= 6.5 +/-.5sqr41

=about 3.3, 9.7

the irrational factors are about

w-3.3 and w-9.7

26=2(9.7+3.3) = 2(13)=26

32 = about 9.7(3.3) = about 32

if this is really a factoring problem

it was either miscopied or misprinted

there's a problem with the problem

if it had been A=32

and P=24 then

w^2 -12w +32 =0 has integer factors

(w-8)(w-4) = 0

w= 4 feet

L= 8 feet