The length of the hypotenuse of a right triangle is 3b. the lengths of the legs are 4a and 3a. write and expression that defines b in terms of a. keep the numerical coefficient in fraction form.
B=?A
example to make it b = 1/2a
To find the value of b in terms of a, we can use the Pythagorean theorem which states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.
In this case, we have:
(4a)^2 + (3a)^2 = (3b)^2
16a^2 + 9a^2 = 9b^2
25a^2 = 9b^2
To isolate b, we can divide both sides of the equation by 9:
b^2 = 25a^2 / 9
Taking the square root of both sides, we get:
b = sqrt(25a^2 / 9)
Simplifying further, we have:
b = (5a / 3)
Therefore, b is equal to (5a / 3) in terms of a.