Question

May someone please help me with this complex math ahhh! I have to find the length and the width of the garden etc.

Answer 1

L = 10.037

W = 2.291

LW = 23..........Equation 1

L = 7W - 6.......Equation 2

*Substitute the value of L to the first equation to solve for W

`LW=23`
`(7W-6)W=23`
`7W^2-6W=23`
`7W^2-6W-23=0`

Through quadratic formula, we can get:

`W=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(7)(-23)}}{2(7)}`
`W=\frac{6\pm2\sqrt[]{170}}{14}`
`W=\frac{3\pm\sqrt[]{170}}{7}`
`W=2.291,\text{ }W=-1.434`

*Since we cannot have a negative value for the dimensions, we will consider 2.291.

Going back to the second equation, substitute the value of W to solve for L.

`L=7W-6`
`L=7(2.291)-6`
`L=10.037`

The length of the garden should be 10.037 feet, and the width should be 2.291 feet.