Word Problem: Triangle

Question

Here is the question:

A triangle has a perimeter of $46$ meters. The length of the second side is $5$ meters more than the length of the first side. The third side is three meters less than twice the first side. How long is each side?

So I obtained the $3$ equations needed for the triangle, which is put together here: $x+(x+5)+(2x-3x)=46$. However,I am having trouble moving forward. What do I do next?

Answer 1

$x+(x+5)+(2x-3)=46$ !!

now you need to solve for x, by first add all the x up together and the numbers aswell:

$(x+x+2x)+(5-3)=46$

$4x + 2 = 46$

now get all the numbers to the right side:

$4x = 46 - 2$

and divide by the factor of x, which is 4

$x = 44/4$

$x = 11$

Answer 2

Draw a picture.

Let the perimeter $P=a+b+c=46$ meters where

$$a= x ~\text{meters}$$ $$b= x+5 ~\text{meters}$$ $$c= 2x-3 ~\text{meters}$$

then

$$P=x+(x+5)+(2x-3)=46~\text{meters}$$

which reduces to

$$4x=44 ~\text{meters} \implies x=11 ~\text{meters}$$

so that

$$a= 11 ~\text{meters}$$ $$b= 16 ~\text{meters}$$ $$c= 19 ~\text{meters}$$