Question

Claire is shopping for a new flat-screen television the day after Thanksgiving.
She found a model that is 23 inches tall and 41 inches wide.
What is the size of the TV, to the nearest inch, as measured along its diagonal?

Answer 1

The size of the TV measured along its diagonal is 47 inches.

Step-by-step explanation:

Step 1:

The TV is in the shape of a rectangle. It has a length of 41 inches and a width of 23 inches.

The rectangle can be split into two right-angled triangles.

According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the square of the other two sides. The diagonal is the hypotenuse of the triangles drawn.

Step 2:

Assume the hypotenuse is x inches long.

So according to the Pythagorean theorem, $x^{2} = 41^{2} +23^{2} = 2,210.$

$x^{2} = 2210, x = 47.0106.$

Rounding this off, we get the value of the diagonal as 47 inches.