Question

Does a triangle with side lengths 7, StartRoot 80 EndRoot, and StartRoot 31 EndRoot from a right triangle?

Answer 1

Answer:

Square of the longest side: 80

Sum of squares of two shorter sides: 80

Yes

Step-by-step explanation:

7, sqrt(80) , sqrt(31)

(sqrt80)² = 7² + (sqrt31)²

80 = 49 + 31

80 = 80

Satisfies pythagoras theorem,

Hence forms a right angle triangle.

Square of the longest side: 80

Sum of squares of two shorter sides: 80

Answer 2

Answer and Step-by-step explanation:

The sides we have are 7, $\sqrt{80}$ , and $\sqrt{31}$ .

The square root of 80 is less than 9 but greater than 8 (because $8^2$ is 64, $9^2$ is 81, and 80 is in between those two values), and the square root of 31 is definitely less than the square root of 80.

So, $\sqrt{80}$ is the longest side.

1) The square of $\sqrt{80}$ is: $(\sqrt{80} )^2=80$

2) The sum of the squares of the two shorter sides is:

$7^2+(\sqrt{31} )^2=49+31=80$

3) Since the square of the longest side is equal to the sum of the squares of the two shorter sides, by the Pythagorean Theorem, the triangle is a right triangles.

Hope this helps!