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)
1 100
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 \( b = 100 \, \text{m} \), \( A = 10 \). Using \( A = \frac{1}{2}bh \), we solve for \( h \):
\( 10 = \frac{1}{2} \times 100 \times h \)
\( 10 = 50h \)
\( h = \frac{10}{50} = 0.2 \).

Step3: Solve for base in Triangle 2

For Triangle 2, height \( h = 0.1 \, \text{m} \), \( A = 10 \). Using \( A = \frac{1}{2}bh \), solve for \( b \):
\( 10 = \frac{1}{2} \times b \times 0.1 \)
\( 10 = 0.05b \)
\( b = \frac{10}{0.05} = 200 \).

Answer:

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

(In the table, Triangle 1 height box: \( 0.2 \), Triangle 2 base box: \( 200 \))