The first side of a triangle is 8m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26m. Find the length of each side

Answer 1

In this problem you have three unknowns. The number of unknowns tells you how many equations you will need to solve the problem.

The first thing you know is that you are working with a triangle and you know the perimeter. So we can set up that equation first.

We allow the following:

x= first side

y=second side

z=third side

The perimeter is each side added to one another, therefore we get our first equation where P=perimeter.

P = x + y + z

Since we know the perimeter, we can say

126 = x + y +z

Next they tell us that x is 8m shorter than y, so we can write the following equation:

x = y - 8 Therefore, we have our second equation.

They tell us that the third side (z) is 4 times as long as x, so we can write

z = 4x

Now we have our three equations!

126 = x + y +z

x = y - 8

z = 4x

Now we have to figure out what to plug in for what. You can really take a lot of different approaches, but my preference is to work with having all x's. You also want to approach it in the least amount of work possible sort of way, so you need the variable that is in all three equations. Therefore, I'm going to take my second two equations and solve for the opposite variables, so that when I plug it back into the first equation, I will only have the variable of x.

The third eqaution is already good to go! So I move to the second.

x = y - 8

All I need to do is add 8 to both sides giving me

y = x + 8

So now, I have my last two equations that look like

y = x + 8

z = 4x

And we have our first equation that looks like

x + y + z = 26

So now I can plug in values for my y and z

x + (x + 8) + 4x = 26

Combining like terms gives me

6x + 8 = 126 Subtracting 8 from both sides I get

6x = 18

x = 3

So now I know that x is equal to 3, I can use the value to solve either of the equations, total choice on which to go to first, but I may as well continue the order.

y = x + 8

y = 3 + 8

y = 11

I now can go to my last equation

z = 4x

z = 4(3)

z = 12

So now I have my three values and I can double check my work by going back to the first equation,

3 + 11 + 12 = 26

Answer 2

Let F=1st side, S = 2nd side and T = 3rd side

F=S-8

T=4F

Perimeter = 32 = S + (S-8) + 4(S-8)

6S = 72

S=12

You go from here!