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
Using the Pythagorean theorem, we know that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the two legs (a and b).
So, using this information, we have:
(c)^2 = (a)^2 + (b)^2
Substituting the given lengths of the legs and hypotenuse, we have:
(3b)^2 = (4a)^2 + (3a)^2
Simplifying, we get:
9b^2 = 16a^2 + 9a^2
Combining like terms, we can write this as:
9b^2 = 25a^2
To solve for b, we take the square root of both sides:
√(9b^2) = √(25a^2)
Simplifying, we have:
3b = 5a
To find b in terms of a, we divide both sides of the equation by 3:
b = 5a/3
Therefore, the expression that defines b in terms of a is b = 5a/3.