Answer:
Properties of Isosceles triangle:
It has two two equal side length.
Corresponding angles to these sides are equal.
As per the statement:
The triangle PHJ as shown in the figure.
Here, HP = 3x-6 unit and PJ = x+2 units
Since, the angles [tex]\angle PHJ[/tex] and [tex]\angle PJH[/tex] are equal
then;
by Properties of Isosceles triangle, we have;
[tex]HP = PJ[/tex]
⇒[tex]3x-6 = x+2[/tex]
Subtract x from both sides we have;
⇒[tex]2x-6 = 2[/tex]
Add 6 to both sides we have;
[tex]2x=8[/tex]
Divide both sides by 2 we have;
x = 4
Substitute in HP we have;
HP = 3x-6 = 3(4)-6= 12-6 = 6
Therefore, the length of HP is, 6 units
