Hypotenuse of a right-angled triangle = 10cm. Perimeter = 28 cm We need to find the area of a right-angled triangle.

Let us denote the lengths of the legs of this right-angled triangle through x and y.

According to the condition of the problem, the hypotenuse of a rectilinear triangle is 10 cm, therefore, using the Pythagorean theorem, we obtain the following relation:

x ^ 2 + y ^ 2 = 100.

It is also known that the perimeter of this right-angled triangle is 28 cm, therefore, the following relationship holds:

x + y + 10 = 28.

Expressing y in terms of from from the second equation, we obtain:

y = 28 – 10 – x;

y = 18 – x.

Substituting this value y into the equation x ^ 2 + y ^ 2 = 100, we get:

x ^ 2 + (18 – x) ^ 2 = 100;

x ^ 2 + 324 – 36x + x ^ 2 = 100;

2x ^ 2 – 36x + 324 – 100 = 0;

2x ^ 2 – 36x + 224 = 0;

x ^ 2 – 18x + 112 = 0;

x = 9 ± √ (81 – 112) = = 9 ± √ (-31).

The discriminant of this quadratic equation is negative, therefore, this equation has no roots.

Consequently, there is no right-angled triangle that satisfies the conditions of the problem.

Answer: there is no right triangle that satisfies the conditions