Answer:
85 units^2 = Area of Blue Square
and
x = 5 units
Step-by-step explanation:
To do this we use the Pythagorean theorem (a^2 + b^2 = c^2). a and b represent the legs of the triangle whereas c represents the longest side of the triangle, or the hypotenuse.
Since we know the area of a square is the side length multiplied by itself (or the side length squared), [tex]\sqrt{35}[/tex] is the side length of the pink square and [tex]\sqrt{50}[/tex] is the side length of the green square.
That means a = [tex]\sqrt{35}[/tex] and b = [tex]\sqrt{50}[/tex] , so...
[tex](\sqrt{35} )^{2} + (\sqrt{50})^{2} = c^{2}[/tex]
35 + 50 = c^2
85 = c^2
[tex]\sqrt{85} = c[/tex]
Now we need to square the square root of 85 to find the area of the blue square.
[tex](\sqrt{85})^{2} = Area of blue square[/tex]
85 units^2 = Area of Blue Square
To solve the other question we use the same formula again.
[tex]x^2 + 12^2 = 13^2\\x^2 +144 = 169\\-144\\x^2 = 25\\x=\sqrt{25} \\x=5[/tex]
x = 5 units
