Show work .

Question

The four blades of a helicopter meet at right angles and are all the same length. The distance between the tips of adjacent (next to) blades is 36 ft. How long is each blade, round your answer to the nearest tenth? Show your work.

Answer 1

√The blades meet at a 90º angle and this forms a right triangle with 2 sides of equal length (b) and a hypotenuse of 36 ft.  The Pythagorean Theorem states that the sum of the squares of the sides of a right triangle equal the square of the hypotenuse.  It is given that 36 ft is the distance between the tips of adjacent blades so 36 ft is the hypotenuse.  The length of each side is b.  Therefore we can write the formula as

 

b² + b² = 36²

 

2b² = 1296  combining like terms and substituting 1296 which is the equivalent of 36 times 36

 

b² = 648   dividing each side of the equation by 2 to get all the unknowns by themselves on the left side

 

b = √648   taking the square root of each side

 

b = 25.5   is the square root of 648 rounded off to the nearest tenth.

 

Each blade is approximately 25.5 feet long. 

 

It is not necessary to look at the rest of the solution I present here.  It is only to show another way to solve the problem (it is a longer way).  I include it to show the principal of factoring the square root.

 

Alternatively, 648 can be factored into 81 X 4 X 2. 

 

The root of a product is equal to the product of its factors or

√abs = √a X √b X √c.

 

To apply this principal, √648 = √81 X √4 X √2

 

9 X 2 X √2 = 18 X √2   substituting 9 for √81 and 2 for √4 

 

We end up with √648 = 18 X √2.

 

Note that 18 X √2 = 25.5.

Answer 2

b = length of a blade

b² + b² = 36²                     The blades are the legs of a right triangle with a hypotenuse of 36.