The length of a rectangle is 7 centimeters less than its width. What are the dimensions of the rectangle if its area is 198 square​ centimeters?

Answer 1

Length x Width = 198

Length = Width - 7

Width - 7 x Width = 198

(w - 7)(w) = 198

Guess and Check

Two numbers with a difference of 7 when multiplied together = 198

19 x 9 = 171. 14 x 14 = 196. Think 2-digit number x 2 digit number with a difference of 7

10 and 17. 11 and 18. 12 and 19. 13 and 20 too much

Try them

10 x 17 = 170

11 x 18 = 198 success

Yes, same as solving for w^2 - 7w - 198

(w + 18 )(w - 11)

Answer 2

width = w

length = w - 7

area = width * length = w(w-7) = 198

w^2 - 7w = 198

w^2 - 7w - 198 = 0

(w - 18)(w+11) = 0

w = 18 or -11

w = 18 (-11 invalid)

width = 18

length = 11

perimeter = 2*length + 2*width = 2*11 + 2*18 = 58