The perimeter of the quadrilateral KORT is 17 cm, KO = 5 cm, OR = 6 cm, RT = KT. Find the length of the side of the CT.

Take a quadrangle KOPT with sides KO; OP; PT and KT. By the condition of the problem, the lengths of the two sides of the quadrilateral are given:

| KO | = 5 (cm);

| OP | = 6 (cm);

and it is known that the lengths of the other two sides are the same:

| PT | = | KT |;

It is also known that the perimeter P of the quadrangle KOPT is 17 cm:

P = 17 (cm);

It is required to find the length of the CT side of the given quadrangle.

Equation for the perimeter of a quadrilateral
Let us denote the lengths of the sides of the quadrangle as a, b and c:

a = | KO | = 5 (cm);

b = | OP | = 6 (cm);

c = | PT | = | KT |;

To solve the problem:

we write the equality for the perimeter P of the quadrangle KOPT;
we get an expression for calculating the length of the side of the CT of the quadrangle;
substitute the initial data and calculate the value of c;
find the perimeter and check the correctness of the obtained solution.
The perimeter of a quadrilateral is the sum of the lengths of all its sides:

P = | KO | + | OR | + | RT | + | CT | = a + b + 2 * c;

From here we find an expression for the unknown quantity c:

2 * c = P – a – b;

c = (P – a – b) / 2;

Determination of the length of the side of the CT
Substituting further into the resulting expression for c with the initial data, we get:

c = (P – a – b) / 2 = (17 – 5 – 6) / 2 = 3 (cm);

Examination:

The perimeter of the KOPT quadrilateral is:

P = a + b + 2 * c = 5 + 6 + 2 * 3 = 17 (cm);

which corresponds to the initial data of the problem.

Answer: the length of the side of the CT is 3 cm.