Triangle Classification Using Sides — Practice Geometry Questions - dummies

Triangle Classification Using Sides — Practice Geometry Questions

By Allen Ma, Amber Kuang

You can classify equilateral, isosceles, scalene, and right triangles based on their side measurements. The following practice questions ask you to identify a triangle using algebra.

Practice questions

Refer to the triangle PER. Use the following information to calculate the length of each side of the triangle and classify the triangle as isosceles, equilateral, scalene, and/or right.

image0.png

  1. The perimeter of

    image1.png

    is 108 units. The three sides of the triangle are represented by

    PE = 5x + 11

    ER = 7x + 1

    RP = 8x – 4

    Classify this triangle.

  2. The perimeter of

    image2.png

    is 60 units. The three sides of the triangle are represented by

    PE = 2a + 8

    ER = 2a – 6

    RP = 3a + 2

    Classify this triangle.

Answers and explanations

  1. Equilateral

    The given perimeter means that all three sides of the triangle add up to 108:

    image3.png

    Find the length of each side of the triangle by plugging in 5 for x:

    image4.png

    Because all three sides of the triangle are equal, the triangle is equilateral.

  2. Scalene right

    The given perimeter means that all three sides of the triangle add up to 60:

    image5.png

    Find the length of each side of the triangle by plugging in 8 for a:

    image6.png

    The three sides of the triangle are all different in length, so the triangle is scalene.

    Because the three sides of the triangle satisfy the Pythagorean theorem, the triangle is also a right triangle:

    image7.png