macy's breakfast table has a square table top with an area of 36 square feet what is the diagonal of the table top

Answer 1

Hello Aliea,

I will first assist you in getting the solution to the above problem, and at the end, I feel it my responsibility as a tutor to provide you several properties of a square. Doing so, may assist you in the future in solving problems such as the one above, and I sincerely apologize in advance if you already know the information. Should you already know it, you can ignore it as it will be near the end, okay?

So, the first step I would take in solving this problem is to determine what the length of the sides are because whether you are dealing with a rectangle the formula for determining the area is A = L x W where A equals area, L equals length, and W equals width. However, with a square, since all sides are equal in length, you can simply use the following equation to determine the perimeter which will give you the measure of the sides, okay?

Therefore:

The area of a square is determined by taking the square root of the Area which is given in this problem. I bring this to your attention simply because I see the mistake made where students will divide the area by four, however doing so will lead you to the wrong conclusion.

Therefore:

Since the Area is 36 square feet, we know the measure of each side - since they will all be equal - is the √36. Therefore, the measure of each side is 6. Do you see how students would end up with the wrong answer should they divide the area by four? They would end up with 9 as the measure leading to the wrong answer, okay?

Now, since we know measure of each side is 6, we can now determine what the hypotenuse or measure of the diagonal is, right? Why? Because we are simply using the Pythagorean Theorem to solve and we already know the measure of two sides. We also know the square forms a 90 degree angle where the legs connect, correct.

Therefore:

a² + b² = d² The reason we are using d squared instead of c squared - which is the Pythagorean Theorem is because they are one and the same, okay?

Therefore:

6² + 6² = d²

36 + 36 = d²

72 = d² <-----In order to isolate d to itself we must take the square root of the left removing

the exponent on the right, okay?

√72 = d

8.485 OR 8.49 = d <-----We simply rounded here. Remember five or above, give it a shove. Four or below, let it go.

Now, we need to check our work, okay? We do so by substituting the values we have arrived at to determine whether the left side equals the right, fair enough?

Therefore:

a² + b² = d²

6² + 6² = d²

36 + 36 = d²

72 = d²

√72 = d²

8.49 = d

I hope this assists and that you have a great ending to your week. Please feel free to leave feedback, seek clarity, or would like to ask additional questions, just click the "add comment' leaving your feedback beneath this solution. Should you need one on one tutoring, please feel free to reach out to me or any tutor.

Now, about that information I would like to share with you which are the properties of a square.

A square is both a rhombus and rectangle and inherits properties of both.

Each of the interior angles is 90 degrees

The diagonals of a square bisect each other

The opposite sides are parallel

A square whose side length is "s" has an area of s²

A square with a side length of "s" has a diagonal measure of s√2

These properties can easily be remembered if you memorize them. Have a great day and again, I apologize for being verbose but feel it my responsibility as a tutor to give you as much information which will, in turn, allow you the needed information so you can solve easily. Best!