Question 51065
Side a of a triangle is 4cm longer than side b. side c is twice as long as side b. What is the length of each side of the triangle if its perimeter is 28cm? p=a+b+c
First: What side do we know nothing about? side b.
So, we describe the other two sides in terms of b.
Side a of a triangle is 4cm longer than side b.
So, side a = b + 4
And we already said we know nothing about side b.
So, side b = b
Side c is twice as long as side b.
So, side c = 2b
Does this make sense so far?
Now lets combine these variables acording to the perimeter formula.
a + b + c = P
So...
b + 4 + b + 2b = 28
Now we can simplify and solve for b.
If we combine like terms we get...
4 + 4b = 28
Subtract 4 from each side to isolate the variable.
4b = 24
Now we can divide both sides by 4.
b = 6
Now that we know the value for b we can solve the word problem.
a = b + 4
a = 6 + 4
a = 10
And...
c = 2b
c = 2(6)
c = 12
so...
a = 10
b = 6
c = 12
We can check by addind these solutions together...
10 + 6 + 12 = 28
Correct!
I hope this helps.
Good Luck!