Question

A triangle has sides of lengths 27, 79, and 84. Is it a right triangle? Explain.

A.) yes. 27^2 + 79^2 = 84^2
B.) yes. 27^2 + 79^2 ≠ 84^2
C.) no. 27^2 + 79^2 = 84^2
D.) no. 27^2 + 79^2 ≠ 84^2

Answer 1

For a triangle to be right, it has to follow the Pythagorean theorem which states that,
                                 c² = a² + b²
a and b are the shorter legs and c is the hypotenuse. From the given,
                             27² + 79² = 6970    ; 84² = 7056
They are not equal therefore, the answer is letter C. 

Answer 2

Answer:

No.

$27^2 + 79^2 \neq 84^2$

Step-by-step explanation:

For  a triangle to be a right angle triangle:

The two shorter side squared need to add up to longest side squared.

Let a and b are the shortest side and c be the longest then;

You can use Pythagoras theorem;

$a^2+b^2=c^2$

As per the statement:

A triangle has sides of lengths 27, 79, and 84

$29^2+79^2 = 729+6241 = 6970$

$84^2 = 7056$

then;

$29^2+79^2 \neq 84^2$

Therefore, this violate the Pythagoras theorem;

therefore, this triangle is not a right angle triangle.