Use the Pythagoras theorem to find the lengths of the sides of the right triangle 3m, (2m + 8), 5m?

Pythagoras theorem is used to establish a relationship among the sides of a right-angled triangle. It has many applications in real life.

Answer: Using the Pythagoras theorem and the lengths of the sides of the right triangle 3m, (2m + 8), 5m, we get that m = 4 and the side lengths as 12, 16, and 20.

Let's understand the solution in detail.

Explanation:

Given side lengths: 3m, (2m + 8), 5m

Now, we assume that 3m and (2m + 8) are the legs of the triangle and 5m is the hypotenuse.

Now, we use the Pythagoras theorem:

⇒ (3m)² + (2m + 8)² = (5m)²

⇒ 9m² + 4m² + 32m + 64 = 25m²

⇒ 12m² - 32m - 64 = 0

⇒ 3m² - 8m - 16 = 0

Now, solving the above equation using the quadratic formula, we get

m = -4/3 and m = 4.

Since sides can't be negative, m = -4/3 is rejected.

Hence, m = 4 is considered in this case.

Thus, substituting the value of m in the given side lengths, we get 12, 16, and 20.

Hence, solving for the given side lengths of the right triangle, we get that m = 4 and side lengths as 12, 16, and 20.