Question

If JK=2x + 5, KL=5x+3, and JL=x^2, find x. ( assume that K is between J and L)

Answer 1

Given the information, we have the following:

While the whole segment JL = x^2. Therefore, we have the following equation:

$\begin{gathered} JK+KL=JL \\ \Rightarrow(2x+5)+(5x+3)=x^2 \end{gathered}$

Solving for x we get the following:

$\begin{gathered} (2x+5)+(5x+3)=x^2 \\ \Rightarrow7x+8=x^2 \\ \Rightarrow x^2-7x-8=0 \\ \Rightarrow(x+1)(x-8)=0 \end{gathered}$

Given the previous result, we have that x=-1 or x=8. Since JL=x^2, we cannot have that x=-1:

$\begin{gathered} \text{if x=-1} \\ \Rightarrow JL=x^2=(-1)^2=1 \\ JK=2x+5=2(-1)+5=-2+5=3 \\ JLWe would have that JL[tex]\begin{gathered} x=8 \\ JK=2x+5 \\ \Rightarrow JK=2(8)+5=16+5=21 \\ KL=5x+3 \\ \Rightarrow KL=5(8)+3=40+3=43 \\ JL=x^2 \\ \Rightarrow JL=(8)^2=64 \end{gathered}$

Since JK+KL=21+43=64=JL, we have that x=8