A triangle has an area of \( 42 \mathrm{~cm}^{2} \). The height of the triangle is 14 centimeters. What is the length of the base of the triangle?

To find the base of the triangle, you can use the formula for the area of a triangle, which is: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height}. \] You know the area is 42 cm² and the height is 14 cm. Plug these values into the formula: \[ 42 = \frac{1}{2} \times \text{base} \times 14. \] Now, first, multiply the height by \(\frac{1}{2}\): \[ 42 = 7 \times \text{base}. \] Next, divide both sides by 7 to find the base: \[ \text{base} = \frac{42}{7} = 6 \text{ cm}. \] So, the length of the base of the triangle is \(6 \text{ cm}\). --- Triangles have been a fundamental shape in geometry for centuries! The Pythagorean theorem, which relates the sides of right triangles, is a cornerstone of mathematics. In ancient civilizations, triangles were used in architecture and navigation, proving their practicality long before modern technology came into play. Triangles are not just for math problems; they also play a vital role in engineering and design! In bridge construction, for instance, triangles are used to create stable structures that can withstand various forces. Their inherently strong shape spreads weight evenly, making them a go-to choice for architects and engineers around the world!