Question

The longest side of a triangle is 8 cm longer than the shortest side and 5 cm longer than the third side. If the perimeter of the triangle is 53 cm, find the lengths of the three sides.

Answer 1

The shortest side of the triangle is 13 cm, the longest side is 21 cm, and the third side is 16 cm.

Step-by-step explanation:

Let's call the shortest side of the triangle x cm. According to the problem, the longest side is 8 cm longer than the shortest side, so it is x+8 cm. The third side is 5 cm shorter than the longest side, so it is (x+8)-5 cm.

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, we can write the equation:

x + (x+8) + ((x+8)-5) = 53

By simplifying and solving this equation, we find x = 13.

So, the lengths of the three sides of the triangle are:

Shortest side: x = 13 cm

Longest side: x+8 = 13+8 = 21 cm

Third side: (x+8)-5 = (13+8)-5 = 16 cm