Two triangles r the same height. The slope side of triangle A is double the slope of B. how do the lengths of these two triangles compare?
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To compare the lengths of two triangles, we need more information about their dimensions. The fact that the triangles have the same height doesn't provide enough details to make a comparison. However, we can establish a relationship between the slopes of the sides.
Let's say the slope of triangle A is represented by m_A, and the slope of triangle B is represented by m_B. Given that "the slope side of triangle A is double the slope of B," we can write the equation:
m_A = 2m_B
Now, let's assume that the base lengths of the triangles are denoted as b_A for triangle A and b_B for triangle B. The area of a triangle is given by the formula:
Area = (base * height) / 2
Since both triangles have the same height, their areas will be directly proportional to their base lengths:
Area_A = (b_A * h) / 2
Area_B = (b_B * h) / 2
To compare the lengths of the two triangles, we can divide the areas:
Area_A / Area_B = (b_A * h) / (b_B * h)
= b_A / b_B
Therefore, the lengths of the two triangles are directly proportional. Thus, if the slope side of triangle A is double the slope of B, then the length of triangle A's base will be double the length of triangle B's base.