Question

The hypotenuse of a night triangle is 13 inches long. The longer leg is 7 inches longer than the shorter leg. Find the side lengths of the triangleLength of the shorter leg:Length of the longer leg:Length of the hypoteruuse: inches

Answer 1

Let us represent this with a diagram for a better understanding

So from the diagram, let the shorter leg be x, then the longer leg will be x + 7

From Pythagoras theorem,

`\begin{gathered} \text{hyp}^2=opp^2+adj^2 \\ 13^2=x^2+(x+7)^2 \\ 169=x^2+x^2+7x+7x+49 \\ 169=2x^2+14x+49 \\ 2x^2+14x+49-169=0 \\ 2x^2+14x-120=0 \\ 2x^2+24x-10x-120=0 \\ 2x(x+12)-10(x+12)=0 \\ (2x-10)(x+12)=0 \\ 2x=10 \\ x=5\text{ } \\ or \\ x+12=0 \\ x=-12 \\ \end{gathered}`

Since x cannot be negative, we go with x = 5

So the shorter leg x = 5 inches

The longer leg x + 7 = 12 inches

The hypotenuse is 13 inches