Triangles efg and qrs are similar. the length of the sides of efg are 144, 128, and 112. the length of the smallest side of qrs is 280, what is the length of the longest side of qrs?

The answer is:  " 355 " .
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The length of the longest side of ΔQRS is:  " 355 " .
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Explanation:
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Given:
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The smallest side of ΔQRS is 280.
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In ΔEFG,  the smallest side is 112 {compared to "144" and "128"}.

The longest side length of ΔEFG is "144" {compared to "128" and "112"}.

What is the length of the largest side of ΔQRS ?

Both triangles are similar, so the following ratios can be set up to solve the problem:

(the smallest side length of ΔEFG) / (the smallest side length of ΔQRS) =
    (the longest side length of ΔEFG) / (the longest side length of ΔQRS) ;
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  →   112/ 280 = 144 / (the longest side length of  ΔQRS);

We wish to solve for "(the longest side length of  ΔQRS)" ;'
   for which we shall represent with the variable, "x" ;
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  →  Rewrite as:  112/280 = 144/ x ;

Reduce "112/180" to:  "2/5" ; 

and rewrite:  "2/5 = 144/x " ;

Cross multiply:  2x = 5(144) ;

Divide EACH SIDE of the equation by "2" ; to isolate "x" on one side of the equation; & to solve for "x" :
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  2x/ 2  =   ;

    x = 5 * ;

    x = 5 * 71 ;

    x = 355 .
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The answer is:  "355" .
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    The length of the longest side of ΔQRS is:  "355" .
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