Answer:
6m wide
14m long
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.