Question

the area of a rectangular patio is 105 ft². the length of the patio is 8 ft longer than the width of the patio. this can be represented by the equation w² + 8w -105 = 0.what is the width of the patio in feet?A) 8ft B)14ftC)15ftD)7ft

Answer 1

Given that the area of a rectangular patio is 105 ft².

The length of the patio is 8 ft longer than the width of the patio.

The equation is

`w^2+8w-105=0`
`We\text{ know that }8w=15w-7w\text{ and }15*7=105.`

The given equation can be written as follows.

`w^2+15w-7w-105=0`

Taking out the common terms.

`w(w^{}+15)-7(w+15)=0`

`(w^{}+15)(w-7)=0`

`(w^{}+15)=0\text{ or }\mleft(w-7\mright)=0`

`w=-15\text{ or }w=7`

The measure can not be negative.

`w=7\text{ ft.}`

Hence the width of the patio is 7 ft.

Option D is correct.