Question

Which of the images above represent a proof of the Pythagorean Theorem? Explain your choice, and then explain how the figure proves the Pythagorean Theorem.

Figure A: Leg a= 9 units (length) Leg b= 36 units (bottom) Leg c= 64 units (diagonal length) Figure B: Leg a= 25 units (length) Leg b= 144 units (bottom) Leg c= 169 units (diagonal length) Um... I'm not very sure if those are the measurements of the legs/hypo in the picture the measurements are inside of the triangle like area. May someone help ke understand this? I know how to do P.T but I'm not sure if those are the measurements for the triangles. Help me please!!

Answer 1

From the second figure it can be seen that 25 + 144 = 169

This implies that 5^2 + 12^2 = 13^2

This is a right triangle with legs of 5 and 12 and hypothenus of 13.

Answer 2

First considering Figure A

Leg a= 9 units (length) Leg b= 36 units (bottom) Leg c= 64 units (diagonal length)

Square of largest side = c² = (64)²=4096

Sum of squares of two smaller sides = a² + b²

= 9² + (36)²

= 81 + 1296

= 1377

c²≠ a² + b²→Does not prove Pythagorean Theorem

Reading Figure B

Leg a= 25 units (length) Leg b= 144 units (bottom) Leg c= 169 units (diagonal length)

Square of largest side = c² = (169)²=28561

Sum of squares of two smaller sides = a² + b²

= (144)² + (25)²

= 20736 +625

= 21361

c²≠ a² + b²→Does not prove Pythagorean Theorem

But none of above two information,about two image proves pythagorean theorem.

So , Reading image A like this

a²= 9→a=3 units, b²= 36→→b=6 units , c²= 64→→→c= 8 units

Square of largest side = c² = 64

Also, a² + b² = 9 + 36=45

c²≠ a² + b²→Does not prove Pythagorean Theorem

Reading Image B

a²=25→a=5,b²= 144→→b=12 units , c²= 169→→→c= 13 units

Square of largest side = c² = 169

Also, a² + b² = 144 + 25 =169

c²= a² + b²→→ prove Pythagorean Theorem

Hence ,If you read image in the second way described by me, then this figure B proves Pythagorean Theorem.