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Sagot :

loneguy

[tex]\text{Let the side of square 1, square 2 and square 3 be x, y and z respectively.}\\\\\text{Given that,}\\\\\text{Perimeter of square 1,~~ p =100 units.}\\\\\text{So}~ x=\dfrac p 4 = \dfrac{100}4 =25~\text{units.}\\\\\\\text{Area of square 2, a = 225 units}^2\\\\\text{So}~y = \sqrt{a} = \sqrt {225} = 15~ \text{units.}\\\\\text{Use Pythagorean theorem to find z}^2\\\\x^2 =y^2 +z^2 \\\\\implies 25^2 = 15^2 +z^2\\\\\implies z^2 = 625 - 225 = 400\\\\\\[/tex]

[tex]\text{Hence the area of square 3 is 400 units}^2.[/tex]

sqdancefan

Answer:

  400 square units

Step-by-step explanation:

The side length of square 1 is 1/4 of its perimeter, so is 100/4 = 25 units. The area of square 1 is the square of the side length, so is 25² = 625 square units.

The area of square 3 is the difference in the areas of squares 1 and 2. This is due to the Pythagorean theorem.

  area 3 = area 1 - area 2

  area 3 = 625 -225

  area 3 = 400 . . . . square units

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