Question

A rectangle has an area of 8m^2. Its breadth is two metres less than its length. Find the dimensions of the rectangle by setting up and solving an equation.

Please show all working thanks!

Answer 1

Let’s make 2 equations for this...

Let y equal the width and let x equal the length
y= x-2
8= xy

Now, we will plug the y from the first equation into the y for our 2nd equation to get
8= x(x-2)

Now, we distribute the x...
x^2-2x= 8

Bring over the 8 by subtraction
x^2-2x-8= 0

Now, you must factor the expression to get
(x-4)(x+2)= 0

Set each part equal to 0 to find what x equals...

x-4= 0
Add 4 to cancel it out on the left side of the equation...
x=4

x+2= 0
Subtract 2 to cancel out the 2 on the left side of the equation
x= -2
You can cancel out this answer because you cannot have a measurement in the negatives

So, using the answer of x= 4 we can now plug it into our first equation of
y= x-2 to get
y= 4-2
y= 2

So, the answer is
y (the width) equals 2
x (the length) equals 4