Teresi
contestada

the lengths of the sides of a triangle are consecutive even integers. one fourth of the perimeter is one less than the length of the shortest side. find the perimeter of the triangle.

Please help xD

Relax

Respuesta :

mhanifa

Answer:

  • 36

Step-by-step explanation:

Let the shortest side be x, the other sides are x + 2 and x + 4

Perimeter is:

  • P = x + (x + 2) + (x + 4) = 3x + 6

It is given that:

  • 1/4P = x - 1

Substitute and solve for x:

  • 1/4(3x + 6) = x - 1
  • 3x + 6 = 4x - 4
  • 4x - 3x = 6 + 4
  • x = 10

Perimeter is:

  • P = 3*10 + 6
  • P = 36

HERE,

the lengths of the sides of a triangle are consecutive even integers.

If one angle=a

other are=(a+2) and (a+4)

So,

perimeter(p) =a+a+2+a+4=3a+6

But,

one fourth of the perimeter is one less than the length of the shortest side.

[tex]\bold{\dfrac{1}{4}p=a-1 }[/tex]

so,

According to the question,

[tex]\tt{\dfrac{1}{4}(3a+6)=a-1 }[/tex]

[tex]\tt{\dfrac{3a+6}{4}=a-1 }[/tex]

[tex]\tt{4(a-1)=3a+6 }[/tex]

[tex]\tt{ 4a-4=3a+6 }[/tex]

[tex]\tt{4a-3a=6+4 }[/tex]

[tex]\bold{ a=10 }[/tex]

so,

Perimeter (p)=3×10+6=30+6=36

perimeter of the triangle is 36 .

Otras preguntas