Question

Write TWO equations using symbolic language.
The lengths of the sides of a triangle are consecutive odd numbers. What is the length of the longest side if the perimeter is 48?
Let x = length of shortest side

correct answer gets brainlisted ​

Answer 1

Solution:

The length of the sides of triangle are consecutive even numbers. Since, a triangle has three sides, we are assuming the lengths to be:

$\mathrm{x,(x+2),(x+4)}$

Here, we should note that:

• Shortest side = $\rm{x}$
• Longest side = $\mathrm{x+4}$

We are given that, the perimeter of triangle is 48. We know that to calculate perimeter, we will be adding up the sides of the triangle.

$\rightarrow \mathrm{x+(x+2)+(x+4) = 48}$

$\rightarrow \mathrm{3x+6 = 48}$

$\rightarrow \mathrm{3x = 48-6}$

$\rightarrow \mathrm{3x = 42}$

$\rightarrow x = \mathrm{\dfrac{42}{3}}$

$\boxed{\mathrm{x = 14}}$

Hence, we have found the value of $\rm{x}$. We know that the longest side of the triangle is $\mathrm{x+4}$. By substituting the value of x,

$\rightarrow \mathrm{x+4}$

$\rightarrow \mathrm{14+4}$

$\boxed{18}$

Hence, the longest side of the triangle is 18cm.

Know more:

Let us also find the other two sides for additional knowledge.

First side $\rightarrow \mathrm{x = 14}$

Second side $\rightarrow \mathrm{x+2 = 14+2}$

Second side $\rightarrow 16$

Let us also verify our answer using perimeter formula:

$14+16+18 = 48$

$48 = 48$

Hence, verified.

Note:

I think the above question is incorrect. According to me, the sides are consecutive even numbers. Sorry, if any mistakes was done by me!