Question

The length of the garden is 5m longer than its width and the area is 14m². How long is the garden?

Answer 1

`7m`

Explanation:

Let the width of the garden be `a`

Length of the garden `=a+5`

`Area=LxxW`

`=>14=(a+5)xxa`

`=>14=a^2+5a`

`=>0=a^2+5a-14`

`=>0=a^2+7a-2a-14`

`=>0=a(a+7)-2(a+7)`

`=>0=(a-2)(a+7)`

Either `a-2=0 => a=2`

Or `a+7=0 => a=-7`

Width cannot be negative.

So , Width `=2m`

Length `=a+5`

`=> 2+5`

`=> 7m`

Answer 2

`\text{Length of garden}\ =\ 7\ \text{m}`

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Explanation:

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First of all define the variables for length and width of rectangular garden.

Let's say,

`x\ \` be the width of the garden.
Then according to the given statement, the length of the garden is given by `\ \ \ x+5\ \`

Now apply the formula for the area of rectangle, and solve for the `\ \ x`.

``

`\text{Area of rectangle}\ = \ \text{Length} \times \text{Width}`

`14=(x+5)(x)`

By solving for `\ x\`, we get:

`x=2` `" "`and`" "` `x=-7`

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Discared the solution `\ x=-7\` since, it will give us negative length of garden, which is not possible.

So using, `x=2`, the length of garden is:

`\text{Length of garden}\ =\ 2+5\ = \ 7\ text{m}`

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That's it!

Answer 3

Let length of the garden `=L\ m`
It is given that length of the garden is `5\ m` longer than its width

`:.` Width `=(L-5)\ m`

Area of the rectangular garden `A="Length"xx"Width"`

`:.A=Lxx(L-5)=(L^2-5L)\ m^2`

Equating with the given value we get

`(L^2-5L)=14`
`L^2-5L-14=0`

Solving the quadratic using split the middle term we get

`L^2-7L+2L-14=0`
`=>L(L-7)+2(L-7)=0`
`=>(L-7)(L+2)=0`

Roots are found as

1. `(L-7)=0=>L=7`
2. `(L+2)=0=>L=-2`
   Ignoring the second root as length can not be negative, we have

   `L=7\ m`