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Alexxx [7]
3 years ago
6

Solve this for me (geometry)

Mathematics
1 answer:
Zielflug [23.3K]3 years ago
3 0

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.

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