Question

Look at the figure. find the length of HP

Answer 1

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