Triangle Area 21: Calculate the Height X with Base 7

To solve this problem, let's apply the following steps:

• Step 1: Identify the formula for the area of a triangle, which is $A = \frac{1}{2} \times \text{base} \times \text{height}$.
• Step 2: Substitute the known values into the formula: $21 = \frac{1}{2} \times 7 \times x$.
• Step 3: Simplify and solve the equation for $x$.

Now, let's work through each step more precisely:
Step 1: We're given the area formula as $A = \frac{1}{2} \times b \times h$.
Step 2: Substitute in the known values: the area $A = 21$, the base $b = 7$, and the height $h = x$, leading to the equation $21 = \frac{1}{2} \times 7 \times x$.
Step 3: Solve for $x$ – first simplify the multiplication on the right: $21 = \frac{7}{2} \times x$.
Step 4: To isolate $x$, multiply both sides by 2 to get $42 = 7x$.
Step 5: Finally, divide both sides by 7 to solve for $x$: $x = \frac{42}{7} = 6$.

Therefore, the value of $x$ is $6$.