The perimeter of the triangle is 24 inches. the sum of the lengths of its two sides is 160 cm

The perimeter of the triangle is 24 inches. the sum of the lengths of its two sides is 160 cm, and their difference is 200 mm. Find the lengths of the sides of this triangle. Find the lengths of the sides of this triangle?

Let us denote the lengths of the two sides of this triangle by x1 and x2.

In the initial data for this task it is reported that if you add the lengths of these two sides, then the result will be 150 cm, and if you subtract the length of the smaller side from the length of the longer side, then the result will be 200 mm, which is 20 cm, therefore, the following take place ratio:

x1 + x2 = 160;

x1 – x2 = 20.

We solve the resulting system of equations.

Subtracting the second equation from the first, we get:

x1 + x2 – x1 + x2 = 160 – 20;

2×2 = 140;

x2 = 140/2 = 70.

Find x1:

x1 = 20 + x2 = 20 + 70 = 90.

According to the condition of the problem, the perimeter of the triangle is 24 dm, which is 240 cm, therefore, we can find the length of the 3rd side:

240 – 90 – 70 = 150 – 70 = 80.

Answer: the lengths of the sides of this triangle are 70 cm, 80 cm and 90 cm.