a triangle is such that the first side is twice the length of the second side. The third side 4m long. if the perimeter of the triangle is 13m, find the length first and second side

3 answers

1) Let the first side of the triangle be "x"

2) Based on the word problem, the second side is "twice the length of the first" - that means multiply by 2 - so the second side can be represented by "2x"

3) Based on the word problem, the third side is "is 3 more than the first" - that means the addition of 3 - so the third side can be represented by "x+3".

4) Based on the word problem, the total perimeter is "31"

5) Now we can make an algebraic formula to figure out the length of each side: Here we go!

First Side Second Side Third Side Perimeter
x + 2x + (x + 3) = 31

... first add together all of the "x"s

3x + (x + 3) = 31

4x + 3 = 31

... now, let us remove "3" from both sides; since it is "+3" we will subtract "3" from each side

4x + 3 - 3 = 31 - 3

... which leaves us with:

4x = 28

... now, because we have "4x", which is the same as saying "4 times x", we have divide both sides by "4" to remove it from the "x":

4x = 28
4 = 4

.... finally we are left with:

x = 7

Now, we can take "7" and find the sides of our triangle:

1) First side - we said was "x", therefore it is: 7

2) Second side - we said was "2x", which would be 2(7), therefore it is: 14

3) Third side - we said was "x + 3", which would be 7 + 3, therefore it is: 10

Now, to check that we are correct, the three sides should add up to the parameter total we were given, which was "31". Let's check:

7 + 14 + 10 = 31

21 + 10 = 31

31 = 31

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