The area of the square of the leg 6 is 36 square units.
The area of the square of the leg 8 is 64 square units.
The area of the square of the hypotenuse square is 100 square units.
The length of the hypotenuse is 10 units.
Formula Used
Area of square, A = [tex](a)^{2}[/tex]
Here, [tex]a[/tex] is the length of the side of the square.
Pythagoras Theorem is given as,
[tex]h^{2} =p^{2} +b^{2}[/tex]
Here, [tex]h, p, b[/tex] are the hypotenuse, perpendicular, and the base of a right angle triangle respectively.
Area of the Square of the Leg 6
Length of the edge of the square = 6 units
Area of square = 6*6
= 36 square units
Area of the Square of the Leg 8
Length of the edge of the square = 8 units
Area of square = 8*8
= 64 square units
Area of the Hypotenuse Square and the Length of the Hypotenuse
Applying Pythagoras theorem,
[tex]h^{2} = (8)^{2} +(6)^{2}[/tex]
[tex]h^{2} = 64+36[/tex]
[tex]h = \sqrt{100}[/tex]
[tex]h = 10 units[/tex]
Therefore, the area of the hypotenuse square is 100 square units and the length of the hypotenuse comes out to be10 units.
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