The first side of the triangle is 8in 5cm, and the second side is 1m3cm. Find its third side if the perimeter of the triangle is 2m63cm.

The task gives the lengths of the two sides and the perimeter of the triangle. Having entered the designation of the lengths of the sides through a, b and c, and the perimeter through p, these tasks can be formalized, for example, as follows: a = 8 dm 5 cm, b = 1 m 3 cm and p = 2 m 63 cm.Then, you can issue and required briefly: find p. First of all, we will express all the data in centimeters. We have: a = 8 dm 5 cm = 8 * 10 cm + 5 cm = 85 cm; b = 1 m 3 cm = 1 * 100 cm + 3 cm = 103 cm and p = 2 m 63 cm = 2 * 100 cm + 63 cm = 263 cm.
As you know, the perimeter of a triangle is equal to the sum of the lengths of all sides of the triangle, that is, p = a + b + c. Substituting these values ​​into this equality, we have (omit the unit of measurement cm): 263 = 85 + 103 + s or 263 = 188 + s, whence c = 263 – 188 = 75.
Before filling out the answer, you need to check whether a triangle with sides exists. For this purpose, we calculate the semiperimeter; it is equal to p / 2 = 263: 2 = 131.5. Since the inequalities are satisfied 85 <131.5; 103 <131.5 and 75 <131.5, then we conclude: the third side has a length of 75 cm or 7 dm 5 cm.
Answer: 7 dm 5 cm.