Answer: 37 units
Step-by-step explanation:
[tex]Blue=144units^2[/tex] This also works as the height of the triangle.
[tex]Pink=1225units^2[/tex] This also works as the base of the triangle.
Let's call pink ''a'', and blue ''b''. The side we're looking for ''c'' is the hypothenuse.
To find the values of a and b, use the area formula of a square and solve for a side. In this case, since we're going to need the squared values, this step can be omitted.
[tex]Formula: A=s^2[/tex]
[tex]s=\sqrt[]{A}[/tex]
Let's work with Blue.
[tex]s=\sqrt[]{144units^2} \\s=12units[/tex]
Now Pink.
[tex]s=\sqrt[]{1225units^2}\\s=35units[/tex]
So we have a triangle with a base of 35 units and a height of 12 units.
Now let's use the pythagoream's theorem to solve.
[tex]c^2=a^2+b^2\\c=\sqrt[]{a^2+b^2} \\c=\sqrt[]{(12units)^2+(35units)^2}\\c=\sqrt[]{144units^2+1225units^2}\\ c=\sqrt[]{1369units^2}\\ c=37units[/tex]
