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Posts tagged with Proof of Pythagoras

Proving the Pythagoras Rule

June16

The Rule of Pythagoras for right-angled triangles is a core part of most Junior High School Maths courses. It states that the area on the longest side (the hypotenuse) is equal to the sum of the squares on the other two sides: Pythagoras didn’t use algebra to express this theorem, of course. Algebra wasn’t developed […]

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10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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