Question

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

Answer 1

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.

`\bold{(1)/(4)p=a-1 }`

so,

According to the question,

`\tt{(1)/(4)(3a+6)=a-1 }`

`\tt{(3a+6)/(4)=a-1 }`

`\tt{4(a-1)=3a+6 }`

`\tt{ 4a-4=3a+6 }`

`\tt{4a-3a=6+4 }`

`\bold{ a=10 }`

so,

Perimeter (p)=3×10+6=30+6=36

perimeter of the triangle is 36 .

Answer 2

• 36

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