Question

The hypotenuse of a right triangle is 5 m long. The shorter leg is 1 m shorter than the longer leg. Find the side lengths of the triangle.Length of the shorter leg:Length of the longer leg:

Answer 1

Length of the shorter leg: 3 m

Length of the longer leg: 4 m

Step-by-step explanation

Let the length of the longer leg be x.

First, let us make a sketch of the problem:

We can find the value of x by applying the Pythagoras rule:

`a^2+b^2=c^2`

where c = length of the hypotenuse

a, b = length of the other two legs

Hence, we have that:

`\begin{gathered} x^2+(x-1)^2=5^2 \\ x^2+x^2-2x+1=25 \\ 2x^2-2x+1-25=0 \\ 2x^2-2x-24=0 \end{gathered}`

Solve for x by factorizing:

`\begin{gathered} 2x^2-8x+6x-24=0 \\ 2x(x-4)+6(x-4)=0 \\ (2x+6)+(x-4)=0 \\ 2x=-6;x-4=0 \\ x=(-6)/(2)=-3;x=4 \end{gathered}`

Since the length of the leg of a triangle cannot be negative, we have that:

`x=4m`

Hence, the length of the shorter leg is:

`\begin{gathered} 4-1 \\ \Rightarrow3m \end{gathered}`

Therefore, the length of the shorter leg is 3 m and the length of the longer leg is 4 m.