Landscaping License Practice Test

If a triangle measures 3", 4", and 5" on a 1/4" scale, how many bags of grout are needed if one bag covers 100 sq ft?

1. 1 bag

2. 2 bags

3. 3 bags

4. 4 bags

The correct answer is: 1 bag

To determine how many bags of grout are needed, it’s essential to first calculate the area of the triangle. The side lengths of 3", 4", and 5" indicate that this is a right triangle, as they satisfy the Pythagorean theorem (3² + 4² = 5²). Using the formula for the area of a right triangle, which is \(\frac{1}{2} \times \text{base} \times \text{height}\), we can substitute the base and height values. In this case, using 3" as the base and 4" as the height: Area = \(\frac{1}{2} \times 3 \times 4 = 6\) square inches. Given that the scale is 1/4", when calculating the area in actual size, we must convert the dimensions accordingly. The actual dimensions of the triangle at a 1/4" scale would be: - 3" becomes 12" - 4" becomes 16" - 5" becomes 20" Now, we recalculate the area using these actual measurements: Area = \(\frac{1}{2} \times 12 \times