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The sides of a triangle are in the ratio 2: 3 : 4 and its perimeter is 63 m .Find the
dimensions ?

Respuesta :

jtm2588

Answer:

14, 21, 28

Step-by-step explanation:

2x + 3x + 4x = 63

Add like terms

9x = 63

Divide both sides by 9

9x/9 = 63/9

x = 7

Solve for each side by substituting in for x

2x = 2(7) = 14

3x = 3(7) = 21

4x = 4(7) = 28

To check if it is correct, add the three answers together.

14 + 21 + 28 = 63

AadhPrit

Answer:

The dimensions if triangle are 14m, 21m, 28m.

Step-by-step explanation:

Given :

  • [tex]\small\purple\bull[/tex] Ratio of sides of triangle = 2 : 3 : 4
  • [tex]\small\purple\bull[/tex] Perimeter of triangle = 63 m.

[tex]\begin{gathered}\end{gathered}[/tex]

Let the :

  • [tex]\small\purple\bull[/tex] Sides of triangle be = 2x, 3x, 4x
  • [tex]\small\purple\bull[/tex] Perimeter of triangle = 63 m.

[tex]\begin{gathered}\end{gathered}[/tex]

As we know that :

  • Perimeter of triangle = Sum of sides of triangle

[tex]\begin{gathered}\end{gathered}[/tex]

According to the question :

Substituting all the given values in the formula to find the dimensions of triangle :

[tex] \begin{gathered} \qquad\longrightarrow{\sf{Perimeter_{(\triangle)}= Sum \: of \: sides}} \\ \\ \quad\longrightarrow{\sf{63x= 2x + 3x + 4x}} \\ \\ \quad\longrightarrow{\sf{63x= 5x + 4x}} \\ \\ \quad\longrightarrow{\sf{63x= 9x}} \\ \\ \quad\longrightarrow{\sf{x= \frac{63}{9}}} \\ \\ \quad\longrightarrow{\sf{x = 7}} \\ \\ \quad{\star{\underline{\boxed{\sf{\purple{x = 7}}}}}}\end{gathered}[/tex]

Hence, the value of x is 7.

[tex]\begin{gathered}\end{gathered}[/tex]

Thus :

  • [tex]\pink\star[/tex] 2x = 2 × 7 = 14 m
  • [tex]\pink\star[/tex] 3x = 3 × 7 = 21 m
  • [tex]\pink\star[/tex] 4x = 4 × 7 = 28 m

[tex]\rule{300}{2.5}[/tex]