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The shortest side of a triangle is 8 mm less than the length of the middle side. The longest side of the triangle is 10 mm more than the length of the middle side. If the perimeter of the triangle is 125 mm, find the length of each side.
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[tex]\huge{\fcolorbox{maroon}{s} {\large{\fcolorbox{white}{mistyrose}{{\fcolorbox{gold} {White}{Answer}}}}}}[/tex]
Given :
Perimeter of the triangle = 125 mm
To find :
Length of each side of triangle
Solution :
Let the unknown middle side's length be x
As it is given that longest side of triangle is 10mm more than length of middle side i.e. "Add 10 to x" :-
=> Longest side length = x + 10
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It is also given that the shortest side is 8mm less than length of middle side i.e. "subtract 8 from x" :-
=> Shortest side length = x - 8
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Hence we have the representatives of each side of triangle which is x, (x+10) and (x-8) which add up to give is the perimeter of 125. Let's make an algebraic equation to express it and find its answer...
[tex] = > x + (x + 10) + (x - 8) = 125 \\ [/tex]
[tex] = > x + x + 10 + x - 8 = 125[/tex]
[tex] = > x + x +x + 10 - 8 = 125[/tex]
[tex] = > 3x + 2 = 125[/tex]
[tex] = > 3x = 125 - 2[/tex]
[tex] = > 3x = 123[/tex]
[tex] = > x = \frac{123}{3} = 41 \\ [/tex]
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Therefore we have length of each side now,,
Middle side = x = 41mm
Longest side = (x+10) = 41+10 = 51mm
Shortest side = (x-8) = 41 - 8 = 33mm
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Hence, the length of each side of triangle is 41mm, 51mm and 33 mm respectively.