The length of a rectangle is 7 cm less than its width what are the dimensions of the rectangle if its area is 120 cm²

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.