Question
The length of the hypotenuse of a right triangle is 3b . The lengths of the legs are 4a and 3a . Write an expression that defines b in terms of a . Keep the numerical coefficient in fraction form.(1 point)
Answers
GPT 3.5
Let's use the Pythagorean theorem to solve this problem.
According to the Pythagorean theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
So, we have:
(3b)^2 = (4a)^2 + (3a)^2
Expanding both sides, we get:
9b^2 = 16a^2 + 9a^2
Combining like terms, we get:
9b^2 = 25a^2
Now, let's solve for b:
b^2 = 25a^2/9
b = √(25a^2/9)
b = (5a/3)
Therefore, the expression that defines b in terms of a is (5a/3).
According to the Pythagorean theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
So, we have:
(3b)^2 = (4a)^2 + (3a)^2
Expanding both sides, we get:
9b^2 = 16a^2 + 9a^2
Combining like terms, we get:
9b^2 = 25a^2
Now, let's solve for b:
b^2 = 25a^2/9
b = √(25a^2/9)
b = (5a/3)
Therefore, the expression that defines b in terms of a is (5a/3).