Question

a triangle has a base of 5 meters and a height of 12 meters. the area of the triangle is 30 meters². fill in the missing dimensions to create triangles with areas that are equivalent to the given triangle.
triangle base (meters) height (meters)
1 60
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 \( A = 30 \, \text{m}^2 \) for equivalent triangles.

Step2: Solve for height in Triangle 1

For Triangle 1, base \( b = 60 \, \text{m} \), \( A = 30 \). Rearrange the formula: \( \text{height} = \frac{2A}{b} \). Substitute values: \( \text{height} = \frac{2 \times 30}{60} = \frac{60}{60} = 1 \, \text{m} \).

Step3: Solve for base in Triangle 2

For Triangle 2, height \( h = 0.1 \, \text{m} \), \( A = 30 \). Rearrange the formula: \( \text{base} = \frac{2A}{h} \). Substitute values: \( \text{base} = \frac{2 \times 30}{0.1} = \frac{60}{0.1} = 600 \, \text{m} \).

Answer:

Triangle 1 height: \( 1 \) meters, Triangle 2 base: \( 600 \) meters