what is the width of a rectangle whose area is 50cm2 and whose length is double the width?

Answer 1

Hello Mubrarak,

So, the first thing we want to do is to create some expressions which will convey the length and width, especially since you need to have both of them in order to calculate the area. Therefore:

Let the width equal x

Let the length equal 2x

Second, we know the formula or equation for the area of a rectangle is as follows: A = L * W where A equals area, L equals length and W equals the width, fair enough?

Therefore:

A = L* W <-------The equation to determine the area of a rectangle.

50 = x * 2x <--------We merely substituted the expressions we assigned for length and width

50 = 2x² <--------End result of multiplying x and 2x

25 = x² <--------Divided both sides of the equation by 2√

√25 = x <--------In order to eliminate the radical on the right, we take the √ of the left

x = 5 <--------This is the width of the rectangle

Next, in order to determine the length, we simply use the expression we assigned to it at the beginning of the problem which is "2x"

2x = 2(5) = 10 <---------This is the width of the rectangle.

Finally, we need to check our work, okay. We are told in the problem that the area is 50 cm², right? To determine whether we are incorrect or correct, we simply substitute the values we found for both the length and width.

Therefore:

A = L * W

50 = 10 * 5

50 = 50

The solution checks out and is therefore valid. I hope this solution assists you and that you have a great Holiday break. Should you need to leave feedback, ask questions about this solution, or need one on one tutoring, please feel free to reach out to me or any tutor. Best!