The hypotenuese of an isosceles right triangle is 13 inches. the midpoints of its sides are connected to form an inscribed triangle, and this process is repeated, creating a third triangle inscribed in the previous one. find the sum of the areas of these triangles if this process is continued infinitely.

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,

Then the area of isosceles right triangle will be:

Therefore the area is:

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.

Substitute in above formula.

Hence, the Sum of the areas of theses triangles is 169/3.

step-by-step explanation:

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