The sides of a triangle make up an arithmetic progression. its largest side is 28 cm

| March 10, 2021 | education

The sides of a triangle make up an arithmetic progression. its largest side is 28 cm, and its perimeter is 66 cm. Find the smaller side of the triangle.

Arithmetic progression is a sequence of numbers in which each number, starting from the second, is obtained from the previous one by adding a constant number (step) to it:

an = a (n-1) + d, then

since we know the large side of the triangle equal to 28 cm, and the sides of the triangle make up an arithmetic progression, we get

Known member of the sequence (first side) 28, previous (second side) 28 – d. pre-previous (third party) 28 – 2d.

It is known that the perimeter of a triangle is equal to the sum of the lengths of its sides, which means 66 = 28 + (28 – d) + (28 – 2d), 18 = 3d, d = 6.

Substituting the value d, we get: more side 28 cm, then 22 cm and last 16 cm.
Answer: 16 cm



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