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). .

Verified Answer :

C(Area of 1) + (Area 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).

View image calculista