Question

The perimeter of a triangle is 79.75 inches. The second side of the triangle is half as big as the first side. The third side is 7.25 in. greater than the first side. What is the length of the longest side of the triangle?

Answer 1

The Longest side is ofcourse `c`.. as `b=a/2` and `a=a` and `c=a+7.25`

Explanation:

For a starter... just imagine a triangle in your head

Now let that second side you were talking about be `b`.. it is half as big as the `a` side.. which means that `a/2=b` or `2b=a`

The Third side which will be `c` is `7.25 "in"` greater than the first side.. which.. in our case is `a`

Now that means that `a+7.25=c`(It might take some time to understand this)

Now we have all the three sides expressed in one variable
`a` is `a`
`b` is `a/2`
`c` is `a+7.25`

There is no formula for the perimeter of a triangle.. so we always take this

Perimeter of Triangle is `a+b+c`
Where the variables represent a side

Now we know the perimeter we'll just have to find out the sides
Apply the formula

`a+b+c=79.75`

`a+a/2+a+7.25=79.25`

Transfer the `7.25`

`a+a/2+a=79.25-7.25`

That gives us

`a+a/2+a=72`

Now we can also make all the denominators on the left hand side common... but I'm gonna do it by multiplying both sides by `2`

`2(a+a/2+a)=2xx72`

Multiply

`2a+a+2a=144`

`5a=144`

`a=144/5`

`a=28.8`

So.. `a` is `28.8" inches "`

Now the longest side is ofcourse `c` as I explained earlier

`c=a+7.25`

`c=28.8+7.25`

`color(red)(c=36.05" inches "`