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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.
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.