Step-by-step explanation:
Keep in mind that this triangle is a 45-45-90 triangle meaning that it's isosceles
This means that the other side is also equal to s
The best way to solve this is by using the pythagorean theorem
[tex]a^{2}[/tex]+[tex]b^{2}[/tex] = [tex]c^{2}[/tex]
10[tex]\sqrt{2}[/tex] = c (because it's the hypotenuse or the longest side)
s = a
s= b
Substitute the values into the formula stated above
[tex]a^{2}[/tex]+[tex]b^{2}[/tex]= [tex]c^{2}[/tex]
[tex]s^{2}[/tex]+[tex]s^{2}[/tex] =(10[tex]\sqrt{2}[/tex][tex])^{2}[/tex]
Simplify
[tex]2s^{2}[/tex] = [tex](\sqrt{102} )^{2}[/tex]
[tex]2s^{2}[/tex]= 102
Now continue simplifying till you completely solve it
[tex]\frac{2s^{2} }{2}[/tex]= [tex]\frac{102}{2}[/tex]
[tex]s^{2}[/tex]= 51
[tex]\sqrt{s^{2} }[/tex] = [tex]\sqrt{51}[/tex]
s=[tex]\sqrt{51}[/tex]
I hope this helps!!!
