Does a triangle with side lengths 7, StartRoot 80 EndRoot, and StartRoot 31 EndRoot from a right triangle?
Use the drop-down menus to answer the following questions.

What is the square of the longest side?

What is the sum of the squares of the two shorter sides?

Is the triangle a right triangle?

Answer and Step-by-step explanation:

The sides we have are 7, , and .

The square root of 80 is less than 9 but greater than 8 (because is 64, 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, is the longest side.

1) The square of is:

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

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!

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