Ratios and side lengths in relation to triangles

Question

What is the perimeter of a basic 30-60-90 triangle (with side lengths equal to the ratio values)? What is the perimeter of a basic 45-45-90 triangle? What would the answers be in both estimated and simplified form?

What is the ratio of the 30-60-90 triangle’s perimeter to the 45-45-90 triangle’s perimeter? What are the steps to get this answer in both simplified and estimated form? Is this ratio true for all 30-60-90 and 45-45-90 triangles?

Answer 1

The sides of a 30-60-90 right triangle are in ratio 1:sqrt(3):2 Perimeter would be 3 + sqrt(3)

The sides of a 45-45-90 right triangle are in ratio 1:1:sqrt(2) Perimeter would be 2 + sqrt(2)

the ratio of the perimeters would be 3 + sqrt(3) / 2 + sqrt(2). Multiply top and bottom of fraction by 2 - sqrt(2) to express ratio in simplified form.

Answer 2

Hi Stratton. The perimeter of a triangle with angle degrees of 30-60-90 would begin at 1 + square root of 3 + 2, for a total of 3 plus square root of 3, and its multiples.

This is because you would use the Pythagorean Theorem, since 90 degrees means there is a right triangle. So 1 squared + square root of 3 squared = 2 squared.

For 45-45-90 triangles, the perimeter would be 1 + 1 + square root of 2, for a total of 2 + square root of 2, and its multiples. Again, the

Pythagorean Theorem is used.

Don’t hesitate to hire me if you want a regular tutor. Thanks.