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.

$x=\dfrac{20}{4}$

$x=5$

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.