The area of any square is
[tex]A=s^2[/tex]
Where "s" is the length of the side of the square
a)
The given triangle has:
Hypotenuse is c
Two legs of the right angle are 21 cm and 28 cm
The area of the square of side length c is
[tex]A=c^2[/tex]
Then we will use the Pythagorean relationship to find c^2
[tex]\begin{gathered} c^2=(21)^2+(28)^2 \\ c^2=441+784 \\ c^2=1225 \end{gathered}[/tex]
Then the area of the square of side c is 1225 square cm
b)
The given triangle has:
Hypotenuse of length 13 mm
Two legs of the right angle are 5 mm and c
The area of the square of the side length c is
[tex]A=c^2[/tex]
We will use the Pythagorean relationship to find it
[tex]\begin{gathered} (13)^2=(5)^2+c^2 \\ 169=25+c^2 \end{gathered}[/tex]
Subtract 25 from both sides
[tex]\begin{gathered} 169-25=25-25+c^2 \\ 144=c^2 \end{gathered}[/tex]
The area of the square of side length c is 144 square mm
