The area of a rectangle is 144in^2. The length is 4 times greater than the width. Which quadratic equation represents the area of the rectangle?

a) w(w - 4) = 144
b) w(w + 4) = 144
c) w(4w) =144
d) w(4 - w) = 144

The key words are: "4 times greater "

Right.

Thanks

You're welcome.

To find the quadratic equation that represents the area of the rectangle, let's break down the information given and set up the equation step by step.

1. The area of a rectangle is given by the formula: Area = length × width.

2. From the problem, we know that the area is 144in^2. So, we can write the equation: Area = 144.

3. The problem also states that the length is 4 times greater than the width. This can be expressed as: length = 4 × width.

4. Now, substitute the value of the length into the area equation: Area = (4 × width) × width.

5. Simplify the equation by multiplying: Area = 4w^2.

6. Finally, substitute the known area value (144) into the equation: 4w^2 = 144.

Now, we have the quadratic equation representing the area of the rectangle: 4w^2 = 144.

Therefore, the correct answer is (c) w(4w) = 144.