Question

A square floor tile has a diagonal 19 inches long. What is the area of the tile?

Answer 1

Answer : diagonal length = d(x) = √2(x)



The length of the diagonal, d, as a function of x (length of one side) is
given by x^2 + x^2 = d^2, or
d(x) = √(2x^2) = √2(x)

Answer 2

The area of the tile is 180.5in²

To find the area of the tile we need to find the side length of the tile.

The tile takes the shape of a square

and a square has an area represented by

A = l²

Where l is the side length

The diagonal is the hypothenus of the two side length of the square

using Pythagorean theorem

19² = x² + x²

361 = 2x²

x² = 361/2

x² = 180.5

Area of the square = x²

= 180.5 in²