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
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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To find the lengths of the first and second sides of the triangle, let's assign variables:
Let the second side be represented by "x".
Since the first side is twice the length of the second side, we can represent the first side as "2x".
The third side is given as 4 meters.
The perimeter of a triangle is the sum of all its sides. In this case, the perimeter is given as 13 meters. So, we can set up the equation:
Perimeter = First side + Second side + Third side
13 = 2x + x + 4
Combining like terms,
13 = 3x + 4
Next, let's isolate the variable. Subtracting 4 from both sides of the equation, we have:
13 - 4 = 3x
9 = 3x
To find the value of x, divide both sides of the equation by 3:
9/3 = x
x = 3
So, the second side of the triangle has a length of 3 meters.
To find the first side, which is twice the length of the second side, we can substitute the value of x into the equation:
First side = 2x = 2 * 3 = 6 meters
Therefore, the lengths of the first and second sides of the triangle are 6 meters and 3 meters, respectively.