Question

The length of a rectangle is 6 more than two times the width of the rectangle. If the area of the rectangle is 176, what is the length of the rectangle?

Answer 1

The length of the rectangle is `22` unit.

Explanation:

Let `w` be the width of rectangle , then the length is `l=2w+6`.
Area of the rectangle is `l*w =176 or (2w+6)*w=176 or 2w^2+6w-176=0 or w^2+3w-88=0 or (w+11)(w-8)=0 :. w=-11 or w=8`. Width can not be negative quantity, so `w=8; l=8*2+6=22`
The length of the rectangle is `22` unit[Ans]

Answer 2

`22`

Explanation:

Let `color(blue)(w` be the width of the triangle

Then, the length will be `color(red)(2w+6`

`color(brown)("Area of rectangle"=w*h`

Where,

`color(orange)(w="width"`

`color(orange)(l="length"`

As the area of the rectangle is `176`

`rarrcolor(blue)((w))*color(red)((2w+6))=176`

Use distributive property

`color(brown)(a(b+c)=ab+ac`

`rarr2w^2+6w=176`

`rarr2w^2+6w-176=0`

Can be written as (divided each term by `2`)

`rarrw^2+3w-88=0`

Factorize it

`rarr(w+11)(w-8)=0`

From this,we can say that

`w=(-11,8)`

As length cannot be negative,

`color(green)(w=8`

Therefore, the length will be `2(8)+6=22`