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

3 Answers
Mar 6, 2018

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

Mar 6, 2018

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

Explanation:


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

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}

That's it!

Mar 6, 2018

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