How does the Pythagorean theorem link algebra and geometry?

Answer 1

Well, to put it simply, the Pythagorean theorem is an equation to find the measurement of a side of a triangle.Algebra is basically equations, and geometry is the study and measurement of shapes. The equation is a+b=c.

Answer 2

Pythagorean system is

H^2 = a^2 + b^2

In geometry , when knowing the two sides of a right-angled triangle the third side can be calculated.

So if you know the two shorter sides , say a = 3 & b = 4 , then the third hypotenuse can be calculated.

e.g.

H^2 = 3^2 + 4^2

H^2 = 9 + 16

H^2 = 25

H = sqrt(25) = 5

This is the Classic (3,4,5)Pythagorean triangle . Another one is 5,12,13.

Now if you know the hypotenuse and only one of the shorter sides then the other short side can be calculated.

Hence

H^2 = a^2 + b^2

Then

b^2 = H^2 - a^2

Here factoring algebra comes into play.

b^2 = (H - a)(H + a) Note the different signs.

So if we know the hypotenuse , say 13 and the shortest side , say 5.

Then substituting in

b^2 = (13 - 5)(13 + 5)

b^2 = (8)*(18)

b^2 = 144

b = sqrt(144) = 12

So there you have it, a bit of geometry and a bit of algebra. Hope that helps!!!!