SOLUTION: # 7. A small area in front of a building is triangular in shape. The perimeter of the triangle is 49 meters. The second side is one-fourth of the first side in length. The third s

Algebra ->  Expressions-with-variables -> SOLUTION: # 7. A small area in front of a building is triangular in shape. The perimeter of the triangle is 49 meters. The second side is one-fourth of the first side in length. The third s      Log On


   

Question 190615: # 7. A small area in front of a building is triangular in shape. The perimeter of the triangle is 49 meters. The second side is one-fourth of the first side in length. The third side is 4 meters more than the first side. Find the length in meters of each side of the triangular region

Answer by jim_thompson5910(35256) About Me  (Show Source):
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# 7
Q: A small area in front of a building is triangular in shape. The perimeter of the triangle is 49 meters. The second side is one-fourth of the first side in length. The third side is 4 meters more than the first side. Find the length in meters of each side of the triangular region

A:


Let
x = length of first side
y = length of second side
z = length of third side


Since "The second side is one-fourth of the first side in length", this means that y=%281%2F4%29x

Also, since "The third side is 4 meters more than the first side", this means z=x%2B4

Finally, because "The perimeter of the triangle is 49 meters", this tells us that x%2By%2Bz=49


x%2By%2Bz=49 Start with the third equation.


x%2B%281%2F4%29x%2Bx%2B4=49 Plug in y=%281%2F4%29x and z=x%2B4


4%28x%29%2Bcross%284%29%28%281%2Fcross%284%29%29x%29%2B4%28x%29%2B4%284%29=4%2849%29 Multiply EVERY term by the LCD 4 to clear the fraction.


4x%2Bx%2B4x%2B16=196 Distribute and multiply.


9x%2B16=196 Combine like terms on the left side.


9x=196-16 Subtract 16 from both sides.


9x=180 Combine like terms on the right side.


x=%28180%29%2F%289%29 Divide both sides by 9 to isolate x.


x=20 Reduce.


So the length of the first side is 20 meters.


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y=%281%2F4%29x Go back to the first equation


y=%281%2F4%29%2820%29 Plug in x=20


y=20%2F4 Multiply


y=5 Reduce


So the length of the second side is 5 meters.

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z=x%2B4 Move onto the second equation


z=20%2B4 Plug in x=20


z=24 Add


So the third side is 24 meters long.


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Answer:


So the lengths of the three sides are:

First: 20 meters
Second: 5 meters
Third: 24 meters