Question

The hypotenuse of the right triangle is 5 meter long. the shorter leg is 1 Meter shorter than the longer leg. find the side length of the triangle. length of the shorter leg:___ mlength of the longer leg :____mlength of the hypotenuse:____m

Answer 1

Shorter leg = x

Longer leg = x +1

Length of the hypotenuse: 5 m ​

We can use the pythagorean theorem with the information given. Doing so, we have:

`\begin{gathered} a^2+b^2=c^2 \\ (x)^2+(x+1)^2=5^2\text{ (Replacing the values)} \\ x^2+x^2+2x+1=25\text{ (Raising both terms to the power of 2)} \\ x^2+x^2+2x=25-1\text{ (Subtracting 1 from both sides of the equation)} \\ 2x^2+2x=24\text{ (Adding like terms)} \\ 2x^2+2x\text{ }-24=0\text{ (Subtracting 24 from both sides of the equation)} \\ 2(x+4)(x-3)=0\text{ (Factoring)} \\ x1=-4\text{ (Since x=-4 makes the factor (x+4) equal to 0)} \\ x2=3\text{ (Since x=3 makes the factor (x}-3\text{) equal to 0)} \\ \text{ Since we need a positive solution x would be equal to 3} \end{gathered}`

So, the answers would be:

Shorter leg = 3 m

Longer leg = 4 m

Length of the hypotenuse: 5 m