Question

Points are: A= (-2,7)B= (3,5)C= (1,0) To show that the triangle is a right triangle, show that the sum of the squares of the lengths of two sides (the legs) equals the square length of the third side (hypotenuse). What is the sum of the squares of the lengths if the legs?What is the square of length of the hypotenuse of the triangle?

Answer 1

The sum of the squares of the lengths is 58

The square of length of the hypotenuse is 58

From the question, we have

AB² = (-2-3)² +(7-5)²= 25+4 =29

BC² = (3-1)²+(5-0)²=4+25=29

AC² = (-2-1)²+(7-0)² = 9+49 = 58

Here we can see that,

AB²+BC² = AC²

The sum of the squares of the lengths of two sides (the legs) equals the square length of the third side (hypotenuse).

the sum of the squares of the lengths = AB²+BC² =29+29 = 58

the square of length of the hypotenuse= 58

Pythagoras Theorem:

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

To learn more about pythagoras theorem visit: brainly.com/question/343682

#SPJ9