The diagram shows squares 1, 2, and 3 constructed on the sides of a right triangle. . . . . Which statement about the squares must be true?. . A.(Perimeter of 1) + (Perimeter of 2) = (Perimeter of 3). B.(Area of 1) + (Area of 2) = (Perimeter of 3). C.(Area of 1) + (Area of 2) = (Area of 3). D.(Perimeter of 1) + (Perimeter of 2) = (Area of 3). .
see the attached figure to better understand the problem
we know that
Applying the Pythagorean Theorem
\(c^{2}= a^{2} +b^{2}\) ------> equation \(1\)
Area of the square \(1\)
\(A1=a^{2} unit^{2}\)
Area of the square \(2\)
\(A2=b^{2} unit^{2}\)
Area of the square \(3\)
\(A3=c^{2} unit^{2}\)
Substitute the values of A1, A2 and A3 in the equation \(1\)
\(A3=A1+A2\)
therefore
the answer is the option
C.(Area of 1) + (Area of 2) = (Area of 3).