Question

The length of the rectangle is 2 m greater than twice its width. The area of the rectangle is 40 m². What is the length of the rectangle?​

Answer 1

10 meters

Explanation:

Set up equations to represent the problem.

Let L represent the length of the rectangle.
Let W represent the width of the rectangle.

LW = 40 m²

L = 2W + 2

Use substitution to solve the system.

(2W + 2)(W) = 40

(2)(W + 1)(W) = 40

(W + 1)(W) = 20

W² + W = 20

W² + W - 20 = 0

(W + 5)(W - 4) = 0

Solutions of W are -5 and 4; -5 doesn't make sense because the width can't be (-5 meters). The width of the rectangle is 4 meters. Substitute this into our equation for length.

L = 2W + 2

L = 2(4) + 2

L = 10 meters

Answer 2

Answer: Let's say the width of the rectangle is "w" meters.

According to the problem, the length of the rectangle is 2 meters greater than twice its width. Therefore, the length of the rectangle can be expressed as: 2w + 2.

The area of a rectangle is given by multiplying its length and width. We are given that the area of the rectangle is 40 m². Therefore, we can write:

w(2w + 2) = 40

Expanding the left side of the equation, we get:

2w² + 2w = 40

Bringing all the terms to one side, we get a quadratic equation:

2w² + 2w - 40 = 0

Dividing both sides by 2, we get:

w² + w - 20 = 0

This equation can be factored as:

(w + 5)(w - 4) = 0

Therefore, the solutions to this equation are w = -5 and w = 4. Since the width of a rectangle cannot be negative, we reject the solution w = -5. Thus, the width of the rectangle is 4 meters.

Using the expression for the length in terms of the width, we can find the length of the rectangle:

length = 2w + 2 = 2(4) + 2 = 10

Therefore, the length of the rectangle is 10 meters.

Explanation: