Arectangular flower bed is to be 8 m longer than it is wide. the flower bed will have an area of 84 m squared
what will it's dimensions be?

6m wide

14m long

Step-by-step explanation:

Let the length be represented by L.

Let the width be represented by W.

We are given we want the length to be 8 m longer than it's width.

So we want L=8+W.

The area of the rectangle is 84 m squared, this means that LW=84.

So I'm going to substitute L=8+W into LW=84.

LW=84

(8+W)W=84             (L=8W)

So we are going to solve (8+W)W=84 for W.

(8+W)W=84

Distribute:

8W+W^2=84

Rearrange left hand side using commutative property:

W^2+8W=84

Subtract 84 on both sides:

W^2+8W-84=0

Now to factor a quadratic with leading coefficient 1 (assuming it isn't prime) is to find two numbers that multiply to be c=-84 and add up to be b=8.

I'm going to play with factor pairs that multiply to be -84

c=-84=4(-21)=12(-7)=6(-14)

So the number we are looking for is -6 and 14 since -6(14)=-84 and -6+14=8.

The factored form of our equation is:

(W+14)(W-6)=0

This means we need to solve both W+14=0 and W-6=0.

W+14=0

W=-14  (I subtracted 14 on both sides)

W-6=0

W=6 (I added 6 on both sides)

The solution W=-14 makes no sense.

W=6 is the solution for the width.  That is the width is 6 m long.

Now the length is 8 more than the width so the length is 14 m long.

6m wide  and  14m long

Step-by-step explanation:

If a rectangular flower bed is to be 8 m longer than it is wide and the flower bed will have an area of 84 m squared, its dimensions will be 6m wide  by  14m long.

L = length

W = Width