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
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