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.​

Answer 1

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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,

$\sf{perimeter(p)=a+a+2+a+4=3a+6}$

But,

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

• $\boxed{\bold{\dfrac{1}{4}p=a-1 }}$

so,

According to the question,

• $\sf{\dfrac{1}{4}(3a+6)=a-1 }$

• $\sf{\dfrac{3a+6}{4}=a-1 }$

• $\sf{4(a-1)=3a+6 }$

• $\sf{ 4a-4=3a+6 }$

• $\sf{4a-3a=6+4 }$

• $\bold{ a=10 }$

so,

Perimeter (p)=3×10+6=30+6=36

.°.perimeter of the triangle is 36

 

$\sf{\color{aquamarine}{@Smaranika54}}$

Answer 2

Answer:

• 36

Explanation:

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.

So the perimeter of the triangle is 36 cm