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Free_Kalibri [48]
3 years ago
7

Anjeli writes the equation (a+b)2=c2+4(12ab) to begin a proof of the Pythagorean theorem.

Mathematics
2 answers:
gavmur [86]3 years ago
7 0

Answer:

Therefore Anjeli is correct and

(a+b)^{2}=c^{2}+4(\frac{1}{2}ab)  is TRUE.

Step-by-step explanation:

Given:

Label on triangle as ΔABC right angle at C such that

AB = c  .....(Hypotenuse)

AC = b  ....(Longer leg)

BC = a  ....(Shorter leg)

To Prove:

(a+b)^{2}=c^{2}+4(\frac{1}{2}ab)

Proof:

We know, in Right angle triangle ABC by Pythagoras theorem we get,

(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}

Substituting the values we get

AB^{2}=BC^{2}+AC^{2}\\\\c^{2}=a^{2}+b^{2}    ...............( 1 )

Now the Left hand side of what Anjeli wrote is

Left hand side = (a+b)²

 Using identity (A+B)² = A²+ B² + 2AB we get

Left hand side = a²+ b² + 2ab

From ( 1 ) we have c^{2}=a^{2}+b^{2}

Substituting we get

Left hand side = c² + 2ab        ...........................( 2 )

Now,

Right hand side =c^{2}+4(\frac{1}{2}ab)

Dividing 4 by 2 we get  2, hence

Right hand side =c^{2}+2ab  .........................( 3 )

Therefore,

Left hand side = Right hand side          From  ( 2 ) and ( 3 )

(a+b)^{2}=c^{2}+4(\frac{1}{2}ab)      ..True

Therefore Anjeli is correct and

(a+b)^{2}=c^{2}+4(\frac{1}{2}ab)  is TRUE.

RUDIKE [14]3 years ago
3 0

Answer:a+b  c   1/2ab

Step-by-step explanation:

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