The problem involves finding the value of \( x \) given that the areas of two triangles are equal. Let's solve it step by step.
Step 1: Understand the Problem
We are given two triangles:
1. A triangle with base \( 6 \) cm and height \( 8 \) cm.
2. Another triangle with base \( 4 \) cm and height \( x \) cm.
The areas of these two triangles are equal. We need to find the value of \( x \).
Step 2: Formula for the Area of a Triangle
The area \( A \) of a triangle is given by:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
Step 3: Calculate the Area of the First Triangle
For the first triangle:
- Base = \( 6 \) cm
- Height = \( 8 \) cm
Using the area formula:
\[
\text{Area}_1 = \frac{1}{2} \times 6 \times 8 = \frac{1}{2} \times 48 = 24 \text{ cm}^2
\]
Step 4: Set Up the Equation for the Second Triangle
For the second triangle:
- Base = \( 4 \) cm
- Height = \( x \) cm
Using the area formula:
\[
\text{Area}_2 = \frac{1}{2} \times 4 \times x = 2x \text{ cm}^2
\]
Step 5: Equate the Areas
Since the areas of the two triangles are equal:
\[
\text{Area}_1 = \text{Area}_2
\]
\[
24 = 2x
\]
Step 6: Solve for \( x \)
Divide both sides of the equation by 2:
\[
x = \frac{24}{2} = 12
\]
Final Answer:
\[
\boxed{12}
\]
Parent Tip: Review the logic above to help your child master the concept of 10th step worksheet.
