Given A = bh solve for b. A) b = Ah B) b = \frac{h}{A} C) b = \frac{A}{h} D) h = \frac{A}{b} 6) What is the slope between the points (3, 5) and (-2, -4)?
The Correct Answer and Explanation is:
The correct answer is C) b = A/h.
This problem tests a fundamental algebraic skill known as solving a literal equation. A literal equation is an equation that consists primarily of variables, such as the formula for the area of a rectangle, A = bh. The goal, “solve for b,” means we need to rearrange the equation using algebraic rules so that the variable ‘b’ is completely by itself on one side of the equals sign.
We begin with the given equation:
A = bh
In this formula, the variables ‘b’ (base) and ‘h’ (height) are being multiplied together. To isolate ‘b’, we must undo this multiplication. The inverse, or opposite, operation of multiplication is division. The core principle of algebra is that to keep an equation balanced, whatever operation you perform on one side, you must also perform on the other side.
Therefore, to isolate ‘b’, we will divide both sides of the equation by ‘h’:
A / h = (bh) / h
On the right side of the equation, the ‘h’ in the numerator and the ‘h’ in the denominator cancel each other out, because any non-zero number divided by itself equals 1. This leaves ‘b’ by itself:
A / h = b
By the symmetric property of equality, which states that if x = y, then y = x, we can flip the equation to present it in a more conventional format:
b = A / h
Comparing this result to the multiple-choice options, we can see that it matches option C. Option D, while a correct rearrangement of the formula, solves for ‘h’ instead of ‘b’, making it the incorrect answer to this specific question. Options A and B are incorrect because they result from applying the wrong mathematical operations.
