Answer:An equilateral triangle with sides of length 48 inches can be divided into two right triangles by drawing a line from one vertex to the midpoint of the opposite side. The height of the equilateral triangle, or the length of the line segment from the vertex to the midpoint of the opposite side, is equal to the height of each of these right triangles.
Using the Pythagorean theorem, the length of the altitude of each right triangle can be found:
sqrt(48^2 - 24^2) = sqrt(2304) = 48 inches.
The area of each right triangle is 1/2 base * height, or 1/2 * 24 * 48 = 576 square inches.
Since the equilateral triangle is made up of two of these right triangles, the total area of the equilateral triangle is 2 * 576 = 1152 square inches.
Explanation:
An equilateral triangle with sides of length 48 inches can be divided into two right triangles by drawing a line from one vertex to the midpoint of the opposite side. The height of the equilateral triangle, or the length of the line segment from the vertex to the midpoint of the opposite side, is equal to the height of each of these right triangles.
Using the Pythagorean theorem, the length of the altitude of each right triangle can be found:
sqrt(48^2 - 24^2) = sqrt(2304) = 48 inches.
The area of each right triangle is 1/2 base * height, or 1/2 * 24 * 48 = 576 square inches.
Since the equilateral triangle is made up of two of these right triangles, the total area of the equilateral triangle is 2 * 576 = 1152 square inches.