Question

One side of a rectangle is 6 longer than the adjacent side. The area is 187. What are the dimensions?

Answer 1

`17` and `11`

Explanation:

The area of a rectangle is `A=l*w`. We can use variable `x` for `l`, and since we know the other side is `6` longer, we can use `(x+6)` for this side. And we know `A=187`. Inputting these values:
`187=x(x+6)` Distribute:
`187=x^2+6x` Set equal to `0`:
`x^2+6x-187=0` `11,17` are factors of 187 and can be subtracted to `6`, so we can factor the equation:
`(x+17)(x-11)=0`
`17` and `11` work for the situation, so they are the dimensions.

Answer 2

The sides of the rectangle are 11 and 17.

Explanation:

let a,b be the sides of the rectangle with b being the loonger side
`b=a+6`
Thus `a*b` = area of rectangle
`a(a+6) = 187`
`a^2+6a = 187`
`a^2+6a-187 = 0`
`a^2+17a-11a-187 = 0`
`a(a+17)-11(a+17) = 0`
`(a+17)(a-11) = 0`
`a=11` or `-17`
a=positve number
`a=11`
`b=a+6`
`b=11+6=17`

therefore the sides of the rectanlge are 11 and 17.