Question

Look at the figure. find the length of HP

Answer 1

The triangle is isosceles, so the two marked side lengths are equal. Thus, 3x - 6 = x + 2, x = 4.

Answer 2

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 $\angle PHJ$ and $\angle PJH$ are equal

then;

by Properties of Isosceles triangle, we have;

$HP = PJ$

⇒$3x-6 = x+2$

Subtract x from both sides we have;

⇒$2x-6 = 2$

Add 6 to both sides we have;

$2x=8$

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