Answer: The length of the rectangle is 8cm while the width is 15cm.
Step-by-step explanation: The length of the rectangle has been described as 7cm less than it’s width. This means if the width is given as W, then the length would be 7 less than W, that is, length would be W - 7. Also the area has been given as 120. With this bit of information we can now express the area as follows;
Area of a rectangle = L x W
Where area is 120, length is W - 7 and width is W.
120 = (W-7) x W
120 = W^2 - 7W
We rearrange all terms on one side of the equation and we now have
W^2 - 7W - 120 = 0
What we now have is a quadratic equation, and by factorizing we now have
(W + 8) (W - 15) = 0
(W + 8) = 0 and (W - 15) = 0
Hence, either W + 8 = 0 and W = -8
OR W - 15 = 0 and W = 15.
We know that the dimensions of the rectangle cannot be a negative number, so we choose W = 15.
Having calculated that, if the length is given as W - 7, then the length is
L = 15- 7
L = 8
Therefore, the length is 8cm and the width is 15cm.