Question

7 look at the figure. find the length of (overline{hp}).

Explanation:

Step1: Identify equal - side condition

Since the base - angles are equal, the triangle is isosceles and $HP = JP$. So, $3x−6=x + 2$.

Step2: Solve the equation for $x$

Subtract $x$ from both sides: $3x−x−6=x−x + 2$, which simplifies to $2x−6=2$. Then add 6 to both sides: $2x−6 + 6=2 + 6$, giving $2x=8$. Divide both sides by 2: $\frac{2x}{2}=\frac{8}{2}$, so $x = 4$.

Step3: Find the length of $HP$

Substitute $x = 4$ into the expression for $HP$: $HP=3x−6=3\times4−6=12 - 6=6$.

Answer:

6