Question

A triangle has side lengths 24, 32, and 42. is it a right triangle? explain.

Answer 1

Answer:

triangle given is not a right triangle

Step-by-step explanation:

Given:-

- The side lengths of a triangle are given as:

                                     24 , 32 , 42

Find:-

is it a right triangle? explain

Solution:-

- Any triangle which conforms to the pythagorean theorem can be classified as a right angle triangle.

- The Pythagorean theorem states that the square of the longest side length known as hypotenuse (H) should be equal to the sum of square of other two side lengths ( Perpendicular / opposite [ P ] and Base / Adjacent [ B] ).

- This can be mathematically expressed as:

                                     H^2 = P^2 + B^2

- From the given side lengths. The largest side length is hypotenuse H = 42. While P and B can be used interchangeably for the other two side lengths. So using the theorem we have:

                                     42^2 = 32^2 + 24^2

                                     1764 : 1024 + 576

                                    1764 ≠ 1600

- We see that the three side lengths of the triangle does not conform to theorem. So we can conclude that the triangle given is not a right triangle.

                                   

Answer 2

When given 3 triangle sides, to determine if the triangle is acute right or obtuse
square all 3 sides
sum the squares of the 2 shortest sides
compare this sum to the square of the 3rd side
if sum > 3rd side squared it's an acute triangle
if sum = 3rd side squared it's a right triangle
if sum < 3rd side squared it's an obtuse triangle

24 32 42

24*24 = 576
32*32 = 1,024
42*42 = 1,764

Sum of the square of 2 shortest sides = 1,600

Since 1,600 < 1,764 these sides form an obtuse triangle.

Source:
http://www.1728.org/triantest.htm