Question

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). .

Answer 1

C. (Area of 1) + (Area of 2) = (Area of 3)

Answer 2

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).