Answer:
3m and 4m
Explanation:
Let's assume that the two legs of the right angle triangle are represented by the variables "a" and "b". According to the given information:
Hypotenuse (c) = 5m
Perimeter (P) = 12m
In a right angle triangle, the Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs:
c^2 = a^2 + b^2
Since we know the hypotenuse (c = 5m), we can substitute it into the equation:
(5m)^2 = a^2 + b^2
25m^2 = a^2 + b^2 -- (Equation 1)
The perimeter of a triangle is the sum of all its sides:
P = a + b + c
Substituting the given values:
12m = a + b + 5m
12m - 5m = a + b
7m = a + b -- (Equation 2)
We have two equations (Equation 1 and Equation 2) with two unknowns (a and b). We can solve this system of equations to find the lengths of the legs.
From Equation 2, we can express "a" in terms of "b":
a = 7m - b
Substitute this expression into Equation 1:
25m^2 = (7m - b)^2 + b^2
25m^2 = 49m^2 - 14mb + b^2 + b^2
25m^2 - 49m^2 + 14mb - 2b^2 = 0
-24m^2 + 14mb - 2b^2 = 0
12m^2 - 7mb + b^2 = 0
Now we have a quadratic equation. We can solve it using factoring, completing the square, or the quadratic formula. Since we know that the triangle is a right angle triangle, we can assume that the legs are positive values. Therefore, we can discard any negative solutions.
After solving the quadratic equation, we find that the possible values for "a" and "b" are a = 3m and b = 4m, or a = 4m and b = 3m.
So, the lengths of the legs of the right angle triangle are either 3m and 4m or 4m and 3m.