a right triangle has legs of length 3x and 4x and hypotenuse of length 75. What are the lengths of the legs of the triangle.
Pythagorean theorem
(leg)^2 + (leg)^2= (hypoyenuse)^2
(3x)^2 + (4x)^2 =(75)^2
9x^2 +16x^2 = 5625
25x^2=5625 ]:25
x^2=225
x=15
so, first leg is 3*15=45
second leg is 4*15=60.
To find the lengths of the legs of the right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's substitute the given values into the equation:
(3x)^2 + (4x)^2 = 75^2
Simplifying the equation:
9x^2 + 16x^2 = 5625
25x^2 = 5625
Dividing both sides by 25:
x^2 = 225
Taking the square root of both sides:
x = ± 15
Since length can't be negative, we take the positive value:
x = 15
Now we can substitute this value back into the expressions for the lengths of the legs:
The length of the first leg is 3x = 3(15) = 45
The length of the second leg is 4x = 4(15) = 60
Therefore, the lengths of the legs of the right triangle are 45 and 60.
To find the lengths of the legs of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the length of one leg as 'a' and the length of the other leg as 'b'. According to the problem, one leg has a length of 3x and the other leg has a length of 4x. The hypotenuse has a length of 75.
By substituting the values into the Pythagorean theorem, we get the following equation:
(3x)^2 + (4x)^2 = 75^2
Now let's simplify the equation:
9x^2 + 16x^2 = 5625
Combining like terms:
25x^2 = 5625
Divide both sides by 25 to isolate x^2:
x^2 = 225
Taking the square root of both sides gives us:
x = 15
Now that we have the value of x, we can substitute it back into our original expressions for the lengths of the legs.
The length of one leg is 3x, so it becomes 3 * 15 = 45.
The length of the other leg is 4x, so it becomes 4 * 15 = 60.
Therefore, the lengths of the legs of the right triangle are 45 and 60.
Yse the Pythagorean theorem to show that the hypotenuse is
5x = 75
x = 15.
Take it from there