Greetings!
Answer:
Width = 7
Length = 15
Explanation:
Let x be the width value:
Because the length is 8cm bigger than the width(x), this can be shown by:
Length = x + 8
If you recall the equation for the area of a rectangle:
Area = length x width
Simply plug the known values in:
105 = (x + 8) * x
(x * x) + (8 * x) = 105
x² + 8x = 105
Move the +105 to the other side making it a -105, meaning that this is now a quadratic:
x² + 8x - 105 = 0
Factorise this:
(x + 15) ( x - 7)
So x = -15 or x = 7
X has to be 7 because you cannot have a negative measurement.
This means that:
The width = 7
And the length = 7 + 8 = 15
Hope this helps!