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The lengths of the sides of a triangle are in the extended ratio 5: 8:10. The perimeter of the triangle is 115 cm. What are the lengths of the sides?
The lengths of the sides in cm are ____

Respuesta :

Given :

  • The length of the sides of the triangle are in the ratio 5:8:10 .
  • The Perimeter of the Triangle is 115 cm.

To Find :

  • The length of the sides of the triangle.

Solution :

Let us assume the sides be 5x cm, 8x cm and 10x cm.

We know,

[tex]\qquad{ \bold{ \pmb{Sum \: of \: all \: sides \: of \: the \: triangle = Perimeter_{(Triangle)}}}}[/tex]

So, Substituting the values :

[tex]\qquad { \dashrightarrow{ \sf{5x + 8x + 10x = 115}}}[/tex]

[tex]\qquad { \dashrightarrow{ \sf{23x= 115}}}[/tex]

[tex]\qquad { \dashrightarrow{ \sf{ \dfrac{23x}{23} = \dfrac{115}{23} }}}[/tex]

[tex]\qquad { \dashrightarrow{ \bf{ x = 5 }}}[/tex]

Therefore,

The length of the sides of the triangle are :

[tex]\qquad { \dashrightarrow{ \sf{ 5x \: cm= 5 \times 5 \: cm = \bf \: 25\: cm }}}[/tex]

[tex]\qquad { \dashrightarrow{ \sf{ 8x \: cm= 8 \times 5 \: cm = \bf \: 40 \: cm }}}[/tex]

[tex]\qquad { \dashrightarrow{ \sf{ 10x \: cm= 10 \times 5 \: cm = \bf \: 50 \: cm }}}[/tex]

SupremeStrange

Step-by-step explanation:

Given:-

Ratio of sides of triangle is 5:8:10 , with perimeter of 115cm.

To Find :-

Measurement of each side

Solution :-

let the each side be 5x , 8x , 10x respectively

we know that ,

perimeter of triangle = sum of all sides

putting the known values ,

115cm = 5x + 8x + 10x

115/23 = x

5 = x

putting the value of x we get ,

each side is 25cm , 40cm , 50cm

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