The width of a rectangle is 9 units less than the length. If the area is 190 square units, then find the dimensions of the rectangle.

Answer 1

Given:

Width = Length - 9

Area = 190

Area = Length * Width (area of a rectangle)

190 = L (L - 9) (substitution)

190 = L² - 9L (clear parenthesis)

0 = L² - 9L - 190 (let one side equal zero)

0 = (L - 19) (L + 10) (factor the trinomial)

L - 19 = 0, L = 19 units (one possible solution)

L + 10 = 0, L = -10 (negative solution not possible for rectangle)

If L = 19, and W = L - 9

then W = 19 - 9 = 10 units = W