Final answer:
Equations B) b1 = 2A/h - b2 and D) b2= 2A/h - b1, are equivalent to the formula for the area of a trapezoid.
Step-by-step explanation:
The formula for the area of a trapezoid is A = 1/2h (b1 + b2). To determine which equations are equivalent to this formula, we can compare them with the original formula and see if they express the same relationship between the variables. Let's go through the equations one by one:
A) h = 2A/b1 + b2: This equation does not match the original formula. The right-hand side is different.
B) b1 = 2A/h - b2: This equation is equivalent to the original formula. If we multiply both sides by h, we get hb1 = 2A - hb2, which can be rearranged to A = 1/2h (b1 + b2).
C) b2 = 2A/ b1 - h: This equation does not match the original formula. The right-hand side is different.
D) b2= 2A/h - b1: This equation is equivalent to the original formula. If we multiply both sides by h, we get hb2 = 2A - hb1, which can be rearranged to A = 1/2h (b1 + b2).
E) b1 = 2A/b2 - h: This equation does not match the original formula. The right-hand side is different.
Therefore, equations B and D are equivalent to the formula for the area of a trapezoid.