What is the surface area of a cube with an edge length of 8 inches?
The surface area of a cube is given by the formula: 6 times the area of one face.
The area of one face of the cube is simply the edge length squared (A = a²).
So the surface area of the cube is:
6 x (edge length)² = 6 x 8² = 6 x 64 = 384 square inches.
Therefore, the surface area of a cube with an edge length of 8 inches is 384 square inches.
Given two triangles that measure 50 and 80 and a side that measures 4 feet, how many triangles, if any can be constructed?
The given information is not enough to construct any triangle.
In order to construct a triangle, the sum of the lengths of any two sides must be greater than the length of the third side (Triangle Inequality Theorem).
Let's assume that the given measurements of 50 and 80 are the lengths of two sides of a triangle, and the length of 4 feet is the third side. Then we can check if this satisfies the Triangle Inequality Theorem:
- 50 + 80 > 4 => 130 > 4 (true)
- 50 + 4 > 80 => 54 > 80 (false)
- 80 + 4 > 50 => 84 > 50 (true)
The second inequality is not true, as the sum of the lengths of two sides (50 and 4) is not greater than the length of the third side (80).
Therefore, it is impossible to construct any triangles with the given measurements.
Given two triangles that measure 50 and 80 and a side that measures 4 feet, how many triangles, if any can be constructed?
A.) exactly one unique triangle
B.) exactly two unique triangles
C.) exactly three unique triangles
D.) no triangle