Let [tex] s,\ m\, l [/tex] be the short, medium and long side, respectively. If we translate all the information into formulas, we get the following system:
[tex]\begin{cases} l = 2s\\ m=s+3\\ s+m+l = 27 \end{cases}[/tex]
Using the second equation, we can express the middle side in terms of the small one, and reduce the system to two equations in two unknowns:
[tex]\begin{cases} l = 2s\\ s+(s+3)+l = 27 \end{cases}[/tex]
And thus
[tex]\begin{cases} l = 2s\\2s+l = 24 \end{cases}[/tex]
But then again, using the first equation, the third becomes
[tex] 2s+l = 24 \iff l+l = 24 \iff 2l = 24 \iff l=12 [/tex]
So, the longest side is 12. Since the small is half the long, we have [tex] s = 6 [/tex]. Finally, the medium is three more of the small, so we have [tex] m = 6+3 = 9 [/tex]
Answer:
Shorter side is 6 meters, medium side is 9 meters and longest side is 12 meters.
Step-by-step explanation:
Given: The longest side of a triangle is two times the shortest side, while the medium side is 3 meters more than the shortest side. The perimeter is 27 meters.
To find: Dimensions of the triangle.
Solution:
Let the smaller side of the rectangle be x meters.
So, larger side is 2x meters
medium side is [tex]x+3[/tex]
It is given that the perimeter of the rectangle is 27 meters.
So, we have
[tex]x+2x+x+3=27[/tex]
[tex]\implies 4x+3=27[/tex]
[tex]\implies 4x=27-3[/tex]
[tex]\implies 4x=24[/tex]
[tex]\implies x=\frac{24}{4}[/tex]
[tex]\implies x=6[/tex]
Hence, shorter side is 6 meters.
longer side is [tex]2(6)=12[/tex] meters
medium side is [tex]6+3=9[/tex] meters.
