Question

Please help me with this and please show me a step by step

Answer 1

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