The perimeter of the rectangle ABC is 192 dm, the AB side is 21 dm less than the AC side

The perimeter of the rectangle ABC is 192 dm, the AB side is 21 dm less than the AC side, but 36 dm larger than the BC side. Find the length of each side of the triangle ABC

Suppose the speaker side length is x dm.

Since the AB side is 21 dm less, then its length will be equal to: x – 21 dm.

Since AB is more than BC by 36 dm, the length of this side will be:

x – 21 – 36 = x – 57 dm.

The sum of the lengths of all sides is the perimeter, so we get:

x + x – 21 + x – 57 = 192 dm.

3 * x = 192 + 78.

3 * x = 270.

x = 270/3 = 90 dm (length of the speaker side).

x – 21 = 90 – 21 = 69 dm (length of side AB).

x – 57 = 90 – 57 = 33 dm (length of the BC side).

Checking the solution:

90 + 69 + 33 = 90 + 102 = 192 dm.

Answer:

69, 90 and 33 dm, respectively.