Bert and Ernie are missing each other and their friend Big Bird. They want to meet at Big Birds nest which is halfway from their apartments. The distance from Berts apartment to Big Birds Nest is (5x+4) miles away while Ernies apartment to Big Birds nest is (15x-30) miles away. How far are Bert and Ernies apartments from Big Birds nest.

  21 miles

Step-by-step explanation:

Each of the distances is the same, so we have ...

  5x +4 = 15x -30

  34 = 10x

  3.4 = x

Then the distances are ...

  5(3.4) +4 = 21 . . . . miles

Bert and Ernie each live 21 miles from Big Bird's nest.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).