Problem 10 - Introductory Algebra for College Students

Question

A triangle has a base of 6 feet and an area of 30 square feet. Find the triangle's height.

Step-by-Step Solution

Answer

The height of the triangle is 10 feet.

Step 1: Understanding the triangle area formula

The formula for the area of a triangle is A = \(\frac{1}{2} * base * height\). This formula can be rearranged as needed depending on what variable we are trying to find. In this exercise, we are asked to find the height, so the formula should be rearranged to isolate the 'height'.

Step 2: Rearrange the formula to solve for height

To find the height given the base and area, we rearrange the formula as follows: \ height = \(\frac{2 * Area}{base}\)

Step 3: Substitute the given values into the equation

The problem gives us a base of 6 feet and an area of 30 square feet. Substituting these values into the equation from Step 2 gives: \ height = \(\frac{2 * 30}{6}\)

Step 4: Perform the calculation

Next, we perform the division to find the height. Calculating gives: \ height = 10 feet