Question 190615
# 7

Q: <font color=red> 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 </font>


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=(1/4)x}}}


Also, since "The third side is 4 meters more than the first side", this means {{{z=x+4}}}


Finally, because "The perimeter of the triangle is 49 meters", this tells us that {{{x+y+z=49}}}



{{{x+y+z=49}}} Start with the third equation.



{{{x+(1/4)x+x+4=49}}} Plug in {{{y=(1/4)x}}} and {{{z=x+4}}}



{{{4(x)+cross(4)((1/cross(4))x)+4(x)+4(4)=4(49)}}} Multiply EVERY term by the LCD {{{4}}} to clear the fraction.



{{{4x+x+4x+16=196}}} Distribute and multiply.



{{{9x+16=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=(180)/(9)}}} Divide both sides by {{{9}}} to isolate {{{x}}}.



{{{x=20}}} Reduce.



So the length of the first side is 20 meters.



----------------------------------------------



{{{y=(1/4)x}}} Go back to the first equation



{{{y=(1/4)(20)}}} Plug in {{{x=20}}}



{{{y=20/4}}} Multiply



{{{y=5}}} Reduce



So the length of the second side is 5 meters.


----------------------------------------------


{{{z=x+4}}} Move onto the second equation



{{{z=20+4}}} Plug in {{{x=20}}}



{{{z=24}}} Add



So the third side is 24 meters long.



=======================================================

Answer:



So the lengths of the three sides are:


First: 20 meters

Second: 5 meters

Third: 24 meters