Answer:
see explanation
Step-by-step explanation:
The width w is 4 feet longer than two times the length , then
w = 2l + 4
The area (A) of the rectangle is length × width , then
A = l(2l + 4) ← distribute parenthesis
A = 2l² + 4l
Given A = 16
2l² + 4l = 16
Subtract 16 from both sides
2l² + 4l - 16 = 0 ( divide through by 2 )
l² + 2l - 8 = 0 ← in standard form
(l + 4)(l - 2) = 0 ← in factored form
Equate each factor to zero and solve for l
l + 4 = 0 ⇒ l = - 4
l - 2 = 0 ⇒ l = 2
However l > 0 then l = 2
and w = 2l + 4 = 2(2) + 4 = 4 + 4 = 8
The length of the rectangle is 2 feet and
the width is 8 feet
