Question 1111585: the perimeter of the triangle is 50cm. one side is three cm less than 4 times side two. side three is five cm longer than side two. write an expression to represent each side, then write and solve an equation to illustrate the lengths of each side of the triangle.
Answer by duckness73(47)   (Show Source):
You can put this solution on YOUR website! Let "x" represent the length of side 1; let "y" represent the length of side 2; and let "z" represent the length of side 3. Since the entire perimeter of the triangle is 50 cm, we know that:
x + y + z = 50
Since the length of side 1 ("x") is three less than 4 times the length of side 2 ("y"), we have:
x = 4y - 3
Since the length of side 3 ("z") is 5 cm longer than the length of side 2 ("y"), we have:
z = y + 5
So we now have three simultaneous equations with three variables:
x + y + z = 50
x = 4y - 3
z = y + 5
Using substitutions from the last two equations into the first, we have:
(4y - 3) + y + (y + 5) = 50
Gathering like terms, we have:
6y + 2 = 50
Subtracting 2 from both sides, we have:
6y = 48
Dividing both sides by 6, we have:
y = 8
So, we know the length of side 2 ("y") is 8.
Substituting 8 in for y in the other two equations, we have:
x = (4 * 8) - 3
x = 32 - 3
x = 29 so the length of side 1 ("x") is 29
z = 8 + 5
z = 13 so the length of side 3 ("z") is 13
Let's add them all together to make sure that the perimeter is 50:
29 + 8 + 13 = 50 yep, it checks
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