If a, b and c are the lengths of a right triangle and c is the longest side, then:
[tex]a^2+b^2=c^2[/tex]
We have a = 18cm, b = 24cm and c = 30cm. Substitute and check:
[tex]L_s=18^2+24^2=324+576=900\\\\R_s=30^2=900\\\\L_s=R_s[/tex]
The triangle with side lengths of 18cm, 24cm, and 30cm is a right triangle and this can be determined by using the Pythagorean theorem.
Given :
The triangle with side lengths of 18cm, 24cm, and 30 cm.
The following steps can be used to determine the given triangle is a right triangle or not:
Step 1 - The Pythagorean theorem can be used to determine whether the given triangle is a right triangle or not.
Step 2 - According to the Pythagorean theorem, the sum of the square of the two shorter sides of the triangle is equal to the square of the larger side of the triangle that is:
[tex]\rm H^2 = P^2+B^2[/tex]
where H is the hypotenuse, P is the perpendicular, and B is the base of the right angle triangle.
Step 3 - To determine the given triangle is a right angle triangle, the Pythagorean theorem must be satisfied.
[tex]24^2 + 18^2 = 30^2[/tex]
LHS = [tex]24^2+18^2[/tex]
= 576 + 324
= 900
RHS = [tex]30^2[/tex]
= 900
So, LHS is equal to RHS. Therefore, the given triangle is a right angle triangle.
For more information, refer to the link given below:
https://brainly.com/question/13263113
