Answer:
length = 20 ft , width = 14 ft
Explanation:
the area (A) of a rectangle (garden ) is calculated as
A = length × width
let width be w , then length = w + 6 ( 6 ft more than width )
given A = 280 ft² , then
280 = w(w + 6) = w² + 6w ( subtract 280 from both sides )
0 = w² + 6w - 280 ← quadratic equation in standard form
consider the factors of the constant term (- 280) which sum to give the coefficient of the w- term (+ 6)
the factors are + 20 and - 14 , since
+ 20 × - 14 = - 280 and + 20 - 14 = + 6
use these factors to split the w- term
w² + 20w - 14w - 280 = 0 ( factor the first/second and third/fourth terms )
w(w + 20) - 14(w + 20) = 0 ← factor out (w + 20) from both terms
(w + 20)(w - 14) = 0 ← in factored form
equate each factor to zero and solve for w
w + 20 = 0 ⇒ w = - 20
w - 14 = 0 ⇒ w = 14
but w > 0 , then w = 14 and w + 6 = 14 + 6 = 20
length = 20 ft and width = 14 ft