Question

Solve this for me (geometry)

Answer 1

Given:

The figure of triangle GHI and a circle M inscribed in the triangle.

To find:

The perimeter of the triangle.

Solution:

We know that the lengths of the tangent on a circle from same exterior point are always equal.

`JH=HK` (Tangent from point H)

`6x-11=2x+9`

`6x-2x=11+9`

`4x=20`

Divide both sides by 4.

`x=(20)/(4)`

`x=5`

Now,

`JH=6x-11`

`JH=6(5)-11`

`JH=30-11`

`JH=19`

In the same way,

`GJ=GL` (Tangent from point H)

`IK=IL` (Tangent from point H)

From the figure, it is clear that,

`IL=GI-GL`

`IL=40-GJ`

`IL=40-23`

`IL=17`

The perimeter of the triangle GHI is:

`Perimeter=GH+HI+GI`

`Perimeter=(GJ+HJ)+(HK+IK)+(GL+IL)`

`Perimeter=(23+19)+(19+17)+(23+17)`

`Perimeter=118`

Therefore, the perimeter of the triangle GHI is 118 units.