Answer:
length = 50 cm
Step-by-step explanation:
let width be w then length = w + 10
area = w(w + 10) = 2000 , that is
w² + 10w = 2000 ( subtract 2000 from both sides )
w² + 10w - 2000 = 0 ← in standard form
Consider the factors of the constant term (- 2000 ) which sum to give the coefficient of the w- term ( + 10)
the factors are + 50 and - 40 , since
50 × - 40 = - 2000 and sum = 50 - 40 = + 10
(w + 50)(w - 40) = 0 ← in factored form
equate each factor to zero and solve for w
w + 50 = 0 ⇒ w = - 50
w - 40 = 0 ⇒ w = 40
Since w > 0 then w = 40 and
length = w + 10 = 40 + 10 = 50 cm
