Respuesta :
Answer:
The Sum of the areas of theses triangles is 169/3.
Step-by-step explanation:
Consider the provided information.
The hypotenuse of an isosceles right triangle is 13 inches.
Therefore,
[tex]x^2+x^2=169\\2x^2=169\\x=\frac{13}{\sqrt{2} }[/tex]
Then the area of isosceles right triangle will be: [tex]A=\frac{1}{2} x^2[/tex]
Therefore the area is: [tex]A=\frac{169}{4}[/tex]
It is given that sum of the area of these triangles if this process is continued infinitely.
We can find the sum of the area using infinite geometric series formula.
[tex]S=\frac{a}{1-r}[/tex]
Substitute [tex]a=\frac{169}{4} \ and\ r=\frac{1}{4}[/tex] in above formula.
[tex]S=\frac{\frac{169}{4}}{1-\frac{1}{4}}[/tex]
[tex]S=\frac{\frac{169}{4}}{\frac{3}{4}}[/tex]
[tex]S=\frac{169}{3}[/tex]
Hence, the Sum of the areas of theses triangles is 169/3.
