Question

The hypotenuse of a right triangle is twice the length of one of its legs. The length of the other leg is 4 feet. Find the length of the three sides of the triangle. Answer exactly or round to 2 decimal places.Legs are __ feetHypotenuse is __ feet

Answer 1

From the statement of the problem we know that:

• we have a right triangle,

,

• the hypotenuse (H) is twice the length of one of its legs (a), so we write:

$H=2a$

• the other leg (b) has a length:

$b=4$

in feet.

From Pitagoras Theorem we know that:

$H^2=a^2+b^2.$

Replacing the equations for H and b, we have that:

$\begin{gathered} (2a)^2=a^2+4^2, \\ 4a^2=a^2+16. \end{gathered}$

Solving the last equation for a, we get:

$\begin{gathered} 4a^2-a^2=16, \\ 3a^2=16, \\ a^2=\frac{16}{3}, \\ a=\sqrt[]{\frac{16}{3}}, \\ a=\frac{4}{\sqrt[]{3}}\cong2.31. \end{gathered}$

The hypotenuse of the triangle:

$H=2a=2\cdot2.31=4.62.$

Answer

The legs of the triangle are 4 and 2.31 feet and the hypotenuse is 4.62 feet,