Question

An architect is using a 30-60-90 drafting triangle. We know the perimeter of the drafting triangle is 18 inches. What is the approximate length of the

short leg of the triangle rounded to the nearest tenth?
Elimination Tool
Select one answer
Option 1: 5.3 inches
Option 2: 6.6 inches
Option 3: 3.0 inches
Option 4: 3.8 inches

Answer 1

The approximate length of the short leg of the triangle is found by dividing the perimeter by the sum of the side ratios of a 30-60-90 triangle and is approximately 3.8 inches.

Step-by-step explanation:

The student is asking about a 30-60-90 drafting triangle with a known perimeter of 18 inches. In a 30-60-90 triangle, the lengths of the sides are in the ratio of 1 : √3 : 2. To find the short leg of the triangle, we need to divide the perimeter by the sum of the ratios (1 + √3 + 2) and then multiply by 1, which is the relative length of the short leg in this type of triangle.

First, calculate the sum of the ratios: 1 + √3 + 2 ≈ 1 + 1.732 + 2 = 4.732
The perimeter (P) is divided by this sum: P / 4.732 = 18 / 4.732 ≈ 3.8 inches
Therefore, the length of the short leg is approximately 3.8 inches, making Option 4 the correct choice.