8. The lengths of the adjacent sides of a rectangle differ by $4.2 \mathrm{~cm}$, and its perimeter is $23.2 \mathrm{~cm}$. Above the longer side of the rectangle, as the base, an isosceles triangle is drawn on the outside, with its perimeter equal to the perimeter of the rectangle. Determine the lengths of the sides of this triangle?
8. Let $a$ and $b$ be two adjacent sides of a rectangle, where $a > b$.

According to the conditions of the problem, we have:

$2a + 2b = 23.2$ and $a = b + 4.2 \quad 2$ points

from which $b = 3.7$, 3 points

$a = 7.9$. 1 point

Let $x$ be the length of the leg of an isosceles triangle.

Then we have: $7.9 + 2x = 23.2 \quad 1$ point

from which $x = 7.65$. 2 points

The length of the base of the triangle is 7.9 cm, and the length of the leg is $7.65 \text{ cm}$. 1 point

.TOTAL 10 POINTS