Question

The blades of a helicopter's propeller are perpendicular and congruent.

The distance between consecutive blade tips is $24feet$.

Find the length $\left(b\right)$ of each blade.

Answer 1

Illustration of position of helicopter's propeller:

Given that the blades are perpendicular and congruent.

So blades meet at an angle $=90°$

And this forms a right triangle having two sides of equal length $=\left(b\right)$

And then a hypotenuse be $=24ft$

Applying Pythagorean theorem

We know that the Pythagorean theorem for a right angled triangle:

$\Rightarrow \left(Hypotenuse\right)²=\left(opposite\right)²+\left(adjacent\right)²$

$$\begin{gathered} \therefore b²+b²=24² \\ \Rightarrow 2b²=576 \\ \Rightarrow b²=288 \\ \Rightarrow b=\sqrt{288}\left[takingthesquarerootofeachside\right] \\ \Rightarrow b=12\sqrt{2}feetor16.9feetafterroundedofftothenearesttenth. \end{gathered}$$

Hence, the blade is approximately $16.9$ $feet$ long.