Problem 66 - Introductory Algebra for College Students

Question

Will help you prepare for the material covered in the next section. Use \(A=\frac{1}{2} b h\) to find \(h\) if \(A=30\) and \(b=12\)

Step-by-Step Solution

Answer

The height of the triangle is 5 units.

Step 1: Identify the given values

The problem provides the values of the area \(A = 30\) and the base \(b = 12\).

Step 2: Substitute the values into the formula

Substitute the area (\(A = 30\)) and the base (\(b = 12\)) into the formula \(A = \frac{1}{2} b h\), resulting in equation \(30 = \frac{1}{2} \times 12 \times h\).

Step 3: Solve for \(h\)

To isolate \(h\), first simplify the right hand side of the equation by multiplying \(\frac{1}{2}\) by 12, to get \(30 = 6h\). Then, divide both sides of equation by 6 to solve for \(h\), resulting in \(h = \frac{30}{6}\).