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the lengths of the sides of a triangle are in as ratio 3:4:5., find the lengths of the sides of this triangle if its perimeter is 96 cm

Sagot :

wegnerkolmp2741o

Answer:

24,32,40

Step-by-step explanation:

side 1: side2: side3: total

3            4         5         3+4+5=12

The total is the perimeter = 96

96/12 = 8

Multiply each term by 8

side 1: side2: side3: total

3*8       4*8      5*8    12*8

24         32       40        96

Let the sides of the triangle ABC be 3x , 4x and 5x.

  • Where x is a multiple.

Perimeter of triangle = 3x + 4x + 5x

[tex] \bf \rightarrow \: 96 \: = \: 12x[/tex]

[tex]\bf \rightarrow \: \frac{96}{12} \: = \: x \\ [/tex]

[tex]\bf \rightarrow \: \cancel\frac{96}{12} \: ^{8} \: = \: x \\ [/tex]

[tex]\bf \rightarrow \: x \: = \: 8[/tex]

Required sides are :

[tex] \bf \implies \: 3x \: = \: 3 \: \times \: 8 \: = 24[/tex]

[tex]\bf \implies \: 4x \: = \: 4 \: \times \: 8 \: = 32[/tex]

[tex]\bf \implies \: 5x \: = \: 5 \: \times \: 8 \: = 40[/tex]

Hence , the sides of the triangle are 24 , 32 and 40.

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