The perimeter of the triangle is 28m, and its diagonal is 10m. find the sides of the rectangle

Let us denote the lengths of the sides of this rectangular quadrangle by x1 and x2.

In the initial data for this task, it is reported that if you add up the lengths of all sides of this rectangular quadrangle, you get 28 meters, and the diagonal of this geometric figure is 10, therefore, the following relations take place:

2×1 + 2×2 = 28;

x1² + x2² = 10².

We solve the resulting system of equations.

Substituting into the second equation the value x1 = 14 – x2 from the first equation, we get:

(14 – x2) ² + x2² = 100;

196 – 28×2 + x2² + x2² = 100;

2×2² – 28×2 + 196 – 100 = 0;

2×2² – 28×2 + 96 = 0;

x2² – 14×2 + 46 = 0;

x2 = 7 ± √ (49 – 48) = 7 ± √1 = 7 ± 1;

x2_1 = 7 + 1 = 8;

x2_2 = 7 – 1 = 6.

Find x1:

x1_1 = 14 – x2_1 = 14 – 8 = 6;

x1_2 = 14 – x2_2 = 14 – 6 = 8.

Answer: the lengths of the sides are 6 meters and 8 meters.