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.

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!