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The sum of squares of the lengths of the triangle is 130 and the square of the length of the hypotenuse is 65
This is a triangle with 3 sides and one side is called the hypotenuse which faces one of the angles 90°
Analysis:
distance between two points = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
distance AB with coordinates A(-2,4) B(5,0) = [tex]\sqrt{(5 - -2)^{2} + (0 - 4)^{2} }[/tex] = [tex]\sqrt{65}[/tex]
distance AC with coordinates A ( -2,4) C(2,6) = [tex]\sqrt{(2--2)^{2} + (6-4)^{2} }[/tex] = [tex]\sqrt{20}[/tex]
distance BC with coordinates B(5,0) C(2,6) = [tex]\sqrt{(2-5)^{2} + (6-0)^{2} }[/tex] = [tex]\sqrt{45}[/tex]
sum of squares of the lengths = [tex](\sqrt{45} )^{2}[/tex] + [tex](\sqrt{65}) ^{2}[/tex] + [tex](\sqrt{20}) ^{2}[/tex] = 65 + 45 + 20 = 130
the square of the length of the hypotenuse = 65
In conclusion, the sum of the squares of the three length is 130 and the square of the hypotenuse is 65
Learn more about right-angled triangle: brainly.com/question/64787
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