2 The size of a TV is the diagonal
measurement of its screen. Will a
46-inch TV fit in a rectangular cabinet
measuring 32 inches long and
28 inches high? Explain.

Use the Pythagorean Theorem to calculate the length of the sides of a right triangle. A TV cut in half on the diagonal is a right triangle.

a^2 + b^2 = c^2

a is the width of the TV

b is the height of the TV

c is the diagonal size of the TV

a is equal to the length of b plus 15, and c is equal to 75. If we out those values into the formula, we get this:

(b+15)^2 + (b)^2 = (75)^2

Factoring that out, we get:

(b)^2 + 225 + (b)^2 = 5625

Then..

2b^2 = 5625 - 225

2b^2 = 5400

b^2 = 5400/2

b^2 = 2700

b = ✓2700

b = 51.9615242271 (round it to an even 52)

Next, we know that a = b + 15, so a = 67.

Therefore, the width of the TV is 67 inches, the height is 52 inches, the diagonal is 75 inches, and you have a very strangely shaped television with a 1.288 (approximately 5:4) aspect ratio. Older “square” TVs mostly had a 1.33 (4:3) ratio, and new TVs are usually either 16:9 (1.77) or 21:9 (2.33). While it's not impossible that you have an old square TV with a 75 inch diagonal, it's pretty unlikely…

Step-by-step explanation: