Question

a triangle has a base of 5 meters and a height of 4 meters. the area of the triangle is 10 meters². fill in the missing dimensions to create triangles with areas that are equivalent to the given triangle.

triangle	base (meters)	height (meters)
2	□	0.1

Explanation:

Step1: Recall triangle area formula

The area of a triangle is given by \( A = \frac{1}{2} \times \text{base} \times \text{height} \). We know the area \( A = 10 \, \text{m}^2 \) for equivalent triangles.

Step2: Solve for height in Triangle 1

For Triangle 1, base \( b = 100 \, \text{m} \), \( A = 10 \). Rearrange the formula: \( \text{height} = \frac{2A}{b} \). Substitute values: \( \text{height} = \frac{2 \times 10}{100} = \frac{20}{100} = 0.2 \).

Step3: Solve for base in Triangle 2

For Triangle 2, height \( h = 0.1 \, \text{m} \), \( A = 10 \). Rearrange the formula: \( \text{base} = \frac{2A}{h} \). Substitute values: \( \text{base} = \frac{2 \times 10}{0.1} = \frac{20}{0.1} = 200 \).

Answer:

Triangle 1 Height: \( 0.2 \) meters
Triangle 2 Base: \( 200 \) meters