Television sizes are determined by the length of their diagonal measure. Michael just bought a new television. The height of the television is 32 inches and the length is 51 inches. Using the Pythagorean Theorem, what is the size of Michael’s new television? Round your answer to the nearest whole inch (whole number).

Question

Television sizes are determined by the length of their diagonal measure. Michael just bought a new television. The height of the television is 32 inches and the length is 51 inches. Using the Pythagorean Theorem, what is the size of Michael’s new television? Round your answer to the nearest whole inch (whole number).

Part A: What parts of the right triangle have you been given? Are you looking for a leg or the hypotenuse?

Part B: Set-up your equation by substituting the correct numbers into the formula.

Part C: Solve for the missing length. Remember to show ALL work for each step.

Part D: What is the size of the television rounded to the nearest whole inch (whole number)? REMEMBER: We’re looking for the length of the diagonal, as that is the measurement used to determine TV Sizes.

Answer 1

Much Ado about Nothing

simply: H^2 = 32^2 + 51^2 = 3625
H = √3625 = ......

Answer 2

I need a walk through

Answer 3

Part A: The problem states that the height of the television is 32 inches and the length (presumably the width) is 51 inches. Therefore, we are given the lengths of the two legs of the right triangle.

Part B: According to the Pythagorean theorem, which applies to right triangles, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the lengths of the two legs. So, we can set up the equation as follows:

hypotenuse^2 = leg1^2 + leg2^2

Let's substitute the given values into the equation:

hypotenuse^2 = 32^2 + 51^2

Part C: Now, we can solve for the missing length by calculating the value of the hypotenuse squared:

hypotenuse^2 = 1024 + 2601

hypotenuse^2 = 3625

To find the value of the hypotenuse, we need to take the square root of both sides:

hypotenuse = √3625

Using a calculator, we find that the square root of 3625 is approximately 60.21.

Part D: However, we are asked to round the answer to the nearest whole inch. Since we cannot have fractional inches for the size of a television, we round 60.21 to the nearest whole inch, which is 60 inches.

Therefore, the size of Michael's new television, rounded to the nearest whole inch, is 60 inches.