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L 3.1.3 Quiz: TheThe diagram shows squares 1, 2, and 3 constructed on the sides of a righttriangle2Which statement about the squares must be true?A. (Area of 1) + (Area of 2) = (Area of 3)B. (Perimeter of 1) + (Perimeter of 2) = (Area of 3)C. (Perimeter of 1) + (Perimeter of 2) = (Perimeter of 3)D. (Area of 1) + (Area of 2) = (Perimeter of 3)

L 313 Quiz TheThe diagram shows squares 1 2 and 3 constructed on the sides of a righttriangle2Which statement about the squares must be trueA Area of 1 Area of class=

Respuesta :

Let side of square 1 is a, side of square 2 is b and square of side be c.

The area of square is square of side.

Determine the area of square 1, square 2 and square 3.

[tex]A_1=a^2[/tex][tex]A_2=b^2[/tex][tex]A_3=c^2[/tex]

Now consider the right angle triangle formed by three square.

Determine the relation between sides of square by using pythagoras theorem.

[tex]\begin{gathered} c^2=a^2+b^2 \\ A_3=A_1+A_2 \end{gathered}[/tex]

So area of square 3 is equal to sum of area of square 1 and area of square 2.

Correct option is A.