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The triangle is Equilateral thus the sides are same and equal.
So ;
[tex]5x = 3x + 10[/tex]
[tex]5x = 6x - 5[/tex]
[tex]3x + 10 = 6x - 5[/tex]
We just need to solve one the above equations and the value of x .
Then put in all three equations to find the sides .
Let's do it....
[tex]5x = 3x + 10[/tex]
Subtract sides 3x
[tex] - 3x + 5x = - 3x + 3x + 10[/tex]
Simplification
[tex]2x = 10[/tex]
Divide sides by 2
[tex] \frac{2}{2} x = \frac{10}{2} \\ [/tex]
Simplification
[tex]x = 5[/tex]
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It's time to find the sides :
[tex]RS = 6(5) - 5[/tex]
[tex]RS = 30 - 5[/tex]
[tex]RS = 25[/tex]
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[tex]SQ = 3(5) + 10[/tex]
[tex]SQ = 15 + 10[/tex]
[tex]SQ = 25[/tex]
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[tex]RQ = 5(5)[/tex]
[tex]RQ = 25[/tex]
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Actually we knew that the sides of any Equilateral triangle are same.
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