Perimeter of triangle ABC = 38 cm, side AC is 2 times larger than side AB, and side AC is 2 cm less

Perimeter of triangle ABC = 38 cm, side AC is 2 times larger than side AB, and side AC is 2 cm less than side BC. find the sides of the triangle.

Let’s write down given:

Given triangle ABC,

P = 38 cm,

AC is twice the size of the AB side, which means: AC = 2 * AB,

And the BC side is 2 cm larger than the AC side, that is: BC = AC + 2, or BC = 2 * AB + 2.

We need to find all three sides.

First, let’s write down the formula for the perimeter of a triangle:

P = AB + AC + BC,

Let’s substitute the known data:

P = AB + 2 * AB + 2 * AB + 2,

P = 5 * AB + 2,

Substitute the numerical value of the perimeter and find AB:

5 * AB + 2 = 38

5 * AB = 36

AB = 7.2 (cm),

Now let’s find the rest of the sides:

AC = 2 * 7.2 = 14.4 (cm),

BC = 14.4 + 2 = 16.4 (cm).

Answer: AB = 7.2 cm; AC = 14.4 cm; BC = 16.4 cm.