Question

Determine the dimensions(length and width) of a landscape design element.

Answer 1

The statement says two important facts:

The length is 8 more than double the width, and the area is equal to 960 ft^2. So rewrite these facts in equations:

Remember that the pool must be rectangular

`l=8+2w`
`A=l*w`
`l*w=960`

Put the variables on the same side, so reach the next two equations:

`l-2w=8`
`l*w=960`

Now solve one for l, you can choose any equation and any variable, I will clear l from the first equation:

`l=8+2w`

Now replace in the second equation and solve

`(8+2w)*w=960`
`2w^2+8w=960`
`2w^2+8w-960=0`
`w_(1,\:2)=(-8\pm √(8^2-4\cdot \:2\left(-960\right)))/(2\cdot \:2)`
`w_(1,\:2)=(-8\pm \:88)/(2\cdot \:2)`
`w_(1,\:2)=(-8\pm \:88)/(2\cdot \:2)`
`w_1=(-8+88)/(2\cdot \:2),\:w_2=(-8-88)/(2\cdot \:2)`
`w=20,\:w=-24`

We only choose the positive value, so the width is 20 ft

Now replace in the first equation to find the length:

`l=8+2(20)=8+40=48`

So the answer is:

length= 48ft

width=20ft