Respuesta :

calculista

Answer:

The perimeter of the triangle is equal to 36 cm

Step-by-step explanation:

we know that

The inscribed circle contained in the triangle BCA is tangent to the three sides

we have that

BF=BH

CF=CG

AH=AG

step 1

Find CG

we know that

CF=CG

so

CF=7 cm

therefore

CG=7 cm

step 2

Find AG

we know that

CA=AG+CG

we have

CA=15 cm

CG=7 cm

substitute

15=AG+7

AG=15-7=8 cm

step 3

Find AH

Remember that

AG=AH

we have

AG=8 cm

therefore

AH=8 cm

step 4

Find BF

Remember that

BF=BH

BH=3 cm

therefore

BF=3 cm

step 5

Find the perimeter of the triangle

P=AH+BH+BF+CF+CG+AG

substitute the values

P=8+3+3+7+7+8=36 cm

The perimeter of  ΔBCA (triangle BCA) is 36 cm

Perimeter of a triangle

The perimeter of a triangle is the sum of the length of the three sides.

The inscribed circle contained in the triangle BCA is tangent to the three sides

Therefore,

BF = BH = 3 cm

CF = CG = 7 cm

AH = AG = 15 - 7 = 8 cm

Therefore,

perimeter = CA + BC + BA

perimeter = 15 + 3 + 7 + 3 + 8

Therefore,

perimeter = 15 + 10 + 11

perimeter = 15 + 21

perimeter = 36 cm

learn more on perimeter here: https://brainly.com/question/15450681

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