We have a triangle with an aspect ratio of 3: 4: 5. The difference between the longest and shortest

We have a triangle with an aspect ratio of 3: 4: 5. The difference between the longest and shortest sides is 2.4 cm. Find the perimeter.

We know the ratio of the sides of the triangle:

AB: BC: AC = 3: 4: 5.

This means that if we introduce the coefficient of proportionality – p, then the lengths of the sides can be written as follows:

AB = 3p cm;

BC = 4p cm;

AC = 5p cm.

Obviously, the largest side is AC and the smallest is AB.

Let’s compose an equation according to the problem condition:

5p – 3p = 2.4;

2p = 2.4;

p = 2.4: 2;

p = 1.2.

This means: AB = 3 * 1.2 = 3.6 (cm), BC = 4 * 1.2 = 4.8 (cm), AC = 5 * 1.2 = 6 (cm).

The perimeter of this triangle:

PABC = AB + BC + AC = 3.6 + 4.8 + 6 = 14.4 (cm).

Answer: PABC = 14.4 cm.