Question

An artist is using tiles in various geometric shapes to make a mosaic. The two tiles she plans to use are shown below

Tiles
16 in.
8 in.
8 in.
If the two tiles have the same area, what is the length of the triangle's base?

Answer 1

The base length of the triangle must be 16 inches if it has the same area as an 8-inch square tile and we assume the height of the triangle is also 8 inches.

Step-by-step explanation:

The question asks to find the length of the triangle's base, given that it has the same area as a square tile with side lengths of 8 inches. Since the square tile has an area of 64 square inches (8 inches × 8 inches), the triangle must also have an area of 64 square inches.

To find the base length of the triangle, we can use the formula for the area of a triangle: Area = ½ × base × height. If we know the area (64 square inches) and we assume the height is the same as the height of the square (8 inches), we can rearrange the formula to solve for the base: base = (2 × Area) / height = (2 × 64) / 8 = 128 / 8 = 16 inches. Therefore, the triangle's base is 16 inches long if it has the same area as the square tile and the same height.